Question

if x+1/x=√7 , find x^4+1/x^4

Answer 1

$\textbf{\underline{Answer :}}$

Given that,

x + 1/x = √7

Now, squaring both sides, we get

(x + 1/x)² = (√7)²

⇒ x² + 1/x² + 2 = 7

⇒ x² + 1/x² = 5

Again, squaring both sides, we get

(x² + 1/x²)² = 5²

⇒ x⁴ + 1/x⁴ + 2 = 25

⇒ x⁴ + 1/x⁴ = 25 - 2

⇒ x⁴ + 1/x⁴ = 23

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