Question

ifx=1/sqrt5-2 the find x²-1/x².​

Answer 1

We are Given : x = 1/√(5 - 2)

We are asked to Find Out the Value of : x² - 1/x²

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x² - 1/x²

⇒ [1/√(5 - 2)]² - 1/[1/√(5 - 2)]²

⇒ [1/√3]² - 1/[1/√3]²

⇒ 1²/(√3)² - 1/[1²/(√3)²]

⇒ 1/3 - 1/[1/3]

⇒ 1/3 - 3/1

⇒ 1/3 - 9/3

⇒ (1 - 9)/3

⇒ - 8/3