Question Number 114676 by ZiYangLee last updated on 20/Sep/20

If a^(1/2) −a^(−(1/2)) =1, prove that a+a^(−1) =3

Answered by Olaf last updated on 20/Sep/20

(√a)+(1/( (√a))) = 1  ⇒ ((√a)+(1/( (√a))))^2  = 1  a+(1/a)+2 = 1 ⇒ a+a^(−1)  = −1 !  But if (√a)−(1/( (√a))) = 1  ⇒ ((√a)−(1/( (√a))))^2  = 1  a+(1/a)−2 = 1  a+a^(−1)  = 3

Commented byZiYangLee last updated on 20/Sep/20

oops typo haha sry sir