ข้อสอบ PAT 1 - ตุลาคม 2558

ข้อ 16

กำหนดให้ stack A space with rightwards arrow on top และ B with rightwards arrow on top เป็นเวกเตอร์ในระนาบ โดยที่ A with rightwards arrow on top equals 16 i with bar on top space plus a top enclose j และ B with rightwards arrow on top equals 8 italic i with bar on top space plus italic b top enclose italic j เมื่อ a และ b เป็นจำนวนจริง ถ้า open vertical bar A with rightwards arrow on top close vertical bar equals open vertical bar B with rightwards arrow on top close vertical bar space และเวกเตอร์ B with rightwards arrow on top ทำมุม 60 degree กับเวกเตอร์ stack A space with rightwards arrow on top​แล้วค่าของ open parentheses a plus b close parentheses squared เท่ากับข้อใดต่อไปนี้

รีวิว - เสียงตอบรับจากผู้เรียน

เฉลยข้อสอบ

begin mathsize 12px style จากโจทย ์ space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space straight a subscript 2 plus straight a subscript 4 plus straight a subscript 6 plus... plus straight a subscript 50 equals 1275
left parenthesis straight a subscript 1 plus straight d right parenthesis plus left parenthesis straight a subscript 3 plus straight d right parenthesis plus left parenthesis straight a subscript 5 plus straight d right parenthesis plus... plus left parenthesis straight a subscript 49 plus straight d right parenthesis equals 1275 rightwards arrow box enclose 2

นำ space box enclose 2 minus box enclose 1 space thin space thin space thin space thin space thin space straight d plus straight d plus straight d plus... plus straight d equals 0
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space space space space space space space space space space 25 straight d equals 0
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space space space space space space space space space space space straight d equals 0
แสดงว ่ า space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space open curly brackets straight a subscript straight n close curly brackets space เป ็ นลำด ั บคงท ี่ space ท ุ กพจน ์ ม ี ค ่ าเท ่ าก ั น end style

              
begin mathsize 12px style จากโจทย ์ space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space straight a subscript 2 plus straight a subscript 4 plus straight a subscript 6 plus... plus straight a subscript 50 equals 1275
left parenthesis straight a subscript 1 plus straight d right parenthesis plus left parenthesis straight a subscript 3 plus straight d right parenthesis plus left parenthesis straight a subscript 5 plus straight d right parenthesis plus... plus left parenthesis straight a subscript 49 plus straight d right parenthesis equals 1275 rightwards arrow box enclose 2

นำ space box enclose 2 minus box enclose 1 space thin space thin space thin space thin space thin space straight d plus straight d plus straight d plus... plus straight d equals 0
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space space space space space space space space space space 25 straight d equals 0
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space space space space space space space space space space space straight d equals 0
แสดงว ่ า space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space open curly brackets straight a subscript straight n close curly brackets space เป ็ นลำด ั บคงท ี่ space ท ุ กพจน ์ ม ี ค ่ าเท ่ าก ั น end style

begin mathsize 12px style จากโจทย ์ space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space straight a subscript 2 plus straight a subscript 4 plus straight a subscript 6 plus... plus straight a subscript 50 equals 1275
left parenthesis straight a subscript 1 plus straight d right parenthesis plus left parenthesis straight a subscript 3 plus straight d right parenthesis plus left parenthesis straight a subscript 5 plus straight d right parenthesis plus... plus left parenthesis straight a subscript 49 plus straight d right parenthesis equals 1275 rightwards arrow box enclose 2

นำ space box enclose 2 minus box enclose 1 space thin space thin space thin space thin space thin space straight d plus straight d plus straight d plus... plus straight d equals 0
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space space space space space space space space space space 25 straight d equals 0
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space space space space space space space space space space space straight d equals 0
แสดงว ่ า space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space open curly brackets straight a subscript straight n close curly brackets space เป ็ นลำด ั บคงท ี่ space ท ุ กพจน ์ ม ี ค ่ าเท ่ าก ั น end style

begin mathsize 12px style จากโจทย ์ space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space straight a subscript 2 plus straight a subscript 4 plus straight a subscript 6 plus... plus straight a subscript 50 equals 1275
left parenthesis straight a subscript 1 plus straight d right parenthesis plus left parenthesis straight a subscript 3 plus straight d right parenthesis plus left parenthesis straight a subscript 5 plus straight d right parenthesis plus... plus left parenthesis straight a subscript 49 plus straight d right parenthesis equals 1275 rightwards arrow box enclose 2

นำ space box enclose 2 minus box enclose 1 space thin space thin space thin space thin space thin space straight d plus straight d plus straight d plus... plus straight d equals 0
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space space space space space space space space space space 25 straight d equals 0
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space space space space space space space space space space space straight d equals 0
แสดงว ่ า space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space open curly brackets straight a subscript straight n close curly brackets space เป ็ นลำด ั บคงท ี่ space ท ุ กพจน ์ ม ี ค ่ าเท ่ าก ั น end style
begin mathsize 12px style space space space space space space space space space space space space space space space space space space space space space space space space space 2 ab equals straight a squared
space space space space space space space space space space space space space space space space 2 ab minus straight a squared equals 0
space space space space space space space space space space space space space space space open parentheses 2 straight b minus straight a close parentheses straight a equals 0
จะได ้ space thin space thin space thin space thin space thin space 2 straight b minus straight a equals 0 space space space space หร ื อ space space space space straight a equals 0
space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space space straight a equals 2 straight b

ถ ้ า space straight a equals 2 straight b space จาก space box enclose 1 space
จะได ้ space space space space straight b squared equals straight a squared plus 192 space space space space space semicolon space แทน space straight a equals 2 straight b
space space space space space space space space space space space space space straight b squared equals open parentheses 2 straight b close parentheses squared plus 192 end style
begin mathsize 12px style space space space space space space space space space space space space space space straight b squared equals 4 straight b squared plus 192
space space space space space space space space space space space space 3 straight b squared equals negative 192
space space space space space space space space space space thin space thin space เป ็ นไปไม ่ ได ้ space เพราะ space straight b squared greater or equal than 0
ด ั งน ั้ น space thin space thin space thin space thin space thin space straight a not equal to 2 straight b

ถ ้ า space straight a equals 0 space จาก space box enclose 1 space
จะได ้ space space space space straight b squared equals straight a squared plus 192 space space space thin space thin space thin space thin space semicolon space แทน space straight a equals 0 end style
begin mathsize 12px style space space space space space space space space space space space space space straight b squared equals open parentheses 0 close parentheses squared plus 192
space space space space space space space space space space space space space straight b squared equals 192

หาค ่ าของ space open parentheses straight a plus straight b close parentheses squared space space space space space space space space space semicolon space แทนค ่ า space straight a equals 0
space space space space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space open parentheses straight a plus straight b close parentheses squared equals open parentheses 0 plus straight b close parentheses squared
space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals straight b squared space space space space space space space space space space space space space space semicolon space แทนค ่ า space straight b squared
space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals 192 end style

ปิด
ทดลองเรียน