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