If x + y = 24 and x² + y² = 360, then find the value of (x⁴ + x²y² + y⁴).
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Correct answer: A
Explanation
Given:
x + y = 24
x² + y² = 360
By the formula:
x² + y² = (x + y)² − 2xy
x² + x²y² + y² = (x² + y²)² − x²y²
x² + y² = (x + y)² − 2xy
360 = 24² − 2xy
360 = 576 − 2xy
2xy = 216
xy = 108
x²y² = (xy)²
= 108²
= 11664
x² + x²y² + y²
= (x² + y²)² − x²y²
= 360² − 11664
= 129600 − 11664
= 117936