If x + y = 11 and x - y = 5, find x⁴ − y⁴.
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Correct answer: A
Explanation
Given:
x + y = 11
x − y = 5
According to the formula:
x⁴ − y⁴ = (x² − y²)(x² + y²)
x² − y² = (x + y)(x − y)
x² − y² = 11 × 5 = 55
(x + y)² = x² + y² + 2xy
121 = x² + y² + 2xy
(x − y)² = x² + y² − 2xy
25 = x² + y² − 2xy
Add both equations:
121 + 25 = 2(x² + y²)
146 = 2(x² + y²)
x² + y² = 73
x⁴ − y⁴ = (x² − y²)(x² + y²) = 55 × 73 = 4015