Question

express(x^2-1/y^2)(y^2-1/x^2) as a perfect square

Answer 1

$\bold{Answer :}$

Now,

(x² - 1/y²) (y² - 1/x²)

= x²y² - x²/x² - y²/y² + 1/(x²y²)

= (xy)² - 1 - 1 + 1/(xy)²

= (xy)² - 2 + 1/(xy)²

= (xy)² - 2 (xy) (1/xy) + 1/(xy)²

= (xy - 1/xy)², which is a perfect square

We used the identity -

(a - b)² = a² - 2ab + b²

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