Folosim formula (a-b)² = a² -2ab + b²
il scriem pe
9-2√14 = (√7) - 2·√7·√2 + (√2)² = (√7-√2)²
9+2√14 = (√7) + 2·√7·√2 + (√2)² = (√7+√2)²
[tex]a= \sqrt{ (\sqrt{7}- \sqrt{2})^2 } = |\sqrt{7}- \sqrt{2}| = \sqrt{7}- \sqrt{2} \\
b= \sqrt{ (\sqrt{7}+\sqrt{2})^2 } = |\sqrt{7}+ \sqrt{2}| = \sqrt{7}+ \sqrt{2}
[/tex]
(a-b)² = 8
(√7+√2 - (√7-√2)² = 8
(√7+√2 - √7 + √2)² =8
(2√2)² = 4 ·2 = 8
b) (a-b+2√2)^100
calculam (a-b+2√2) = √7 - √2 - (√7 +√2) + 2√2
= √7 - √2 -√7 -√2 + 2√2 = -2√2 + 2√2 = 0
0^100 = 0
