ข้อสอบคณิต O-NET - 2550

ข้อ 3

${(1 - \sqrt{2})}^{2} {(2 + \sqrt{8})}^{2} {(1 + \sqrt{2})}^{3} {(2 - \sqrt{8})}^{3}$ มีค่าเท่ากับข้อใดต่อไปนี้

1
$- 32$
2
$- 24$
3
$- 32 - 16 \sqrt{2}$
4
$- 24 - 16 \sqrt{2}$

รีวิว - เสียงตอบรับจากผู้เรียน

เฉลยข้อสอบ

$จากโจทย์ {(1 - \sqrt{2})}^{2} {(2 + \sqrt{8})}^{2} {(1 + \sqrt{2})}^{3} {(2 - \sqrt{8})}^{3} จะได้ {(1 - \sqrt{2})}^{2} {(2 + 2 \sqrt{2})}^{2} {(1 + \sqrt{2})}^{3} {(2 - 2 \sqrt{2})}^{3} = {(1 - \sqrt{2})}^{2} {[2 (1 + \sqrt{2})]}^{2} {(1 + \sqrt{2})}^{3} {[2 (1 - \sqrt{2})]}^{3}$

$= {(1 - \sqrt{2})}^{2} (4) {(1 + \sqrt{2})}^{2} {(1 + \sqrt{2})}^{3} (8) {(1 - \sqrt{2})}^{3} = 32 {(1 - \sqrt{2})}^{5} {(1 + \sqrt{2})}^{5} = 32 {[(1 - \sqrt{2}) (1 + \sqrt{2})]}^{5} = 32 {(1 - 2)}^{5} = 32 {(- 1)}^{5} = - 32$