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If-a-1-2-a-1-2-1-prove-that-a-a-1-3-

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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
Ifa12−a−12=1,provethata+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
a+1a=1⇒(a+1a)2=1a+1a+2=1⇒a+a−1=−1!Butifa−1a=1⇒(a−1a)2=1a+1a−2=1a+a−1=3
Commented by ZiYangLee last updated on 20/Sep/20
oops typo haha sry sir
oopstypohahasrysir

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