1.

If(a+1/a)^2=3 then show that a^3+1/a^3=0​

Answer»

Step-by-step EXPLANATION:

{(a + \frac{1}{a} )}^{2} = 3 \\ \\ {a}^{3} + \frac{1}{ {a}^{3} } \\ = {(a + \frac{1}{a} )}( {a}^{2} - a \times \frac{1}{a} + \frac{1}{ {a}^{2} } ) \\ = \sqrt{3} \times ((a + \frac{1}{a} ) ^{2} - 2 \times a \times \frac{1}{a} - 1) \\ = \sqrt{3} \times (3 - 3) \\ = \sqrt{3} \times 0 \\ = 0

proved.

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