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EXPLANATION.
⇒ (x + 1/x)² = 3.
As we know that,
We can write equation as ,
⇒ (x + 1/x) = √3.
Cube both sides of the equation, we get.
⇒ (x + 1/x)³ = (√3)³.
⇒ (x³ + 3(x²)(1/x) + 3(x)(1/x²) + 1/x³) = 3√3.
⇒ (x³ + 3x + 3/x + 1/x³) = 3√3.
⇒ (x³ + 3(x + 1/x) + 1/x³) = 3√3.
Put the value of x + 1/x = √3 in equation, we get.
⇒ (x³ + 3(√3) + 1/x³) = 3√3.
⇒ (x³ + 1/x³) = 3√3 - 3√3.
⇒ (x³ + 1/x³) = 0.
Hence proved.
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