Question

(a+1÷a)^2=3 where a is not equal to 0 show that a^3+1÷a^3=0

Answer 1

Hope u like the process,
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HERE WE Go,

Formula to be used:
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x³ + y³ = (x+y) (x² - xy +y²)
(x +y) ² = x² + y² +2xy
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So,

(a + 1/a)² = 3

or, a² + 1/a² +2.a.1/a = 3

or, a² + 1/a² = 3-2

or, a² + 1/a² = 1
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NOW,

-->a³ + 1/a³
= (a +1/a) (a² + 1/a² - a. 1/a)
= ( a +1/a) ( 1 - 1) __(since a² +1/a² =1)_
= 0× ( a +1/a) =0 __(proved) __
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Hope u got it.

Proud to help you.