If x + y = 6 and x² + y² = 20, then find the value of (x⁴ + x²y² + y⁴).
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Correct answer: B
Explanation
Given:
x + y = 6
x² + y² = 20
By the formula:
(x + y)² = x² + y² + 2xy
x² + x²y² + y² = (x² + y²)² − x²y²
(6)² = 20 + 2xy
36 = 20 + 2xy
2xy = 16
xy = 8
x²y² = (xy)² = 64
(x² + y²)² = 20² = 400
x² + x²y² + y² = 400 − 64 = 336