Question

If ( a + 1/a ) 2 = 3 and a ¥ 0 ; then show that :

a3 + 1/a3 = 0 .​

Answer 1

Given (a+1/a) 2 = 3

Therefore (a + 1/a) = √3

Recall the formula, (a3 + b3) = (a + b)3 - 3ab(a + b)

Therefore, (a3 + 1/a3) = (a + 1/a)3 - 3 x a x 1/a (a + 1/a)

= (√3)3 - 3(√3) = 3√3 - 3(√3 = 0