ข้อสอบ A-Level คณิตประยุกต์ 1 ปี 2561 (วิชาสามัญเก่า)

ข้อ 11

จำนวนเต็ม x ที่สอดคล้องกับอสมการ open vertical bar 2 x squared plus 1 close vertical bar minus open vertical bar negative x squared plus 2 x minus 1 close vertical bar less or equal than 15 มีทั้งหมดกี่จำนวน

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เฉลยข้อสอบ

begin mathsize 12px style น ิ ยาม space space space space space space space space space space space space space open vertical bar x close vertical bar space open curly brackets table attributes columnalign left end attributes row cell x space space space space เม ื่ อ space x greater-than or slanted equal to 0 end cell row cell negative x space เม ื่ อ space x less than 0 end cell end table close space end style

begin mathsize 12px style จากโจทย ์ space space space space space space open vertical bar 2 x squared plus 1 close vertical bar minus open vertical bar negative x squared plus 2 x minus 1 close vertical bar less-than or slanted equal to 15 rightwards arrow circle enclose 1
space space space space space space space space space space space space space space space space space space space space space space
minus โดย space 2 x squared plus 1 greater-than or slanted equal to 0 space เสมอ space space space end style

begin mathsize 12px style จะได ้ space space space space space space space space space space space space space open vertical bar 2 x squared plus 1 close vertical bar equals 2 x squared plus 1

minus โดย space minus x squared plus 2 x minus 1 equals negative left parenthesis x squared minus 2 x plus 1 right parenthesis
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 equals negative left parenthesis x minus 1 right parenthesis squared less than 0 space เสมอ space space space space space end style

begin mathsize 12px style จะได ้ space space space space space space space space space space space space space open vertical bar negative x squared plus 2 x minus 1 close vertical bar equals negative open parentheses negative x squared plus 2 x minus 1 close parentheses
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 space space space space space space space space space space thin space thin space equals x squared minus 2 x plus 1 end style

begin mathsize 12px style จาก circle enclose 1 space space space space space space space space space space space open vertical bar 2 x squared plus 1 close vertical bar minus open vertical bar negative x squared plus 2 x minus 1 close vertical bar less-than or slanted equal to 15
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 2 x squared plus 1 minus left parenthesis x squared minus 2 x plus 1 right parenthesis less-than or slanted equal to 15
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 2 x squared plus 1 minus x squared plus 2 x minus 1 less-than or slanted equal to 15
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 space space space space space space space space space space space x squared plus 2 x minus 15 less-than or slanted equal to 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 space space space space space space space space space space left parenthesis x minus 3 right parenthesis left parenthesis x plus 5 right parenthesis less-than or slanted equal to 0 end style
                                                    
                                         begin mathsize 12px style open square brackets negative 5 comma 3 close square brackets end style

begin mathsize 12px style ด ั งน ั้ น thin space thin space thin space thin space thin space thin space จำนวนเต ็ ม space x space ค ื อ space minus sign 5 comma minus sign 4 comma minus sign 3 comma minus sign 2 comma minus sign 1 comma 0 comma 1 comma 2 comma 3
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 ม ี ท ั้ งหมด space 9 space จำนวน end style

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