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if x²+y²=30 xy=5 then x⁴-y⁴=?

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if x²+y²=30 xy=5 then x⁴-y⁴=?

Posted by Gulafshan Nayeem 5 years, 1 month ago

CBSE > Class 09 > Mathematics

1 answers

Ankit Raj 5 years, 1 month ago

Since, x² + y² = 30 ____________(1) & xy = 5 we know that, (x + y)² = x² + y² + 2xy (x + y)² = 30 + 2×5 (x + y)² = 40 (x + y) = √40___________(2) Again (x - y)² = x² + y² - 2xy (x - y)² = 30 - 2×5 (x - y)² = 20 (x - y) = √20____________(3) therefore, (x⁴ - y⁴) = (x² - y²)(x² + y²) = (x - y)(x + y)(x² + y²) = √20×√40×30 = 20√2×30 (x⁴ - y⁴) = 600√2.

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