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Positive numbers $x$ and $y$ have $x^{2} + y^{2} = 25$ and $x y = 12$ . Find $x^{3} + y^{3}$ .

Competition practiceAlgebra

A91
B127
C343
D61

Step-by-Step Solution

(x + y)^{2} = 25 + 24 = 49

, so

x + y = 7

. Then

x^{3} + y^{3} = 7^{3} - 3 \times 12 \times 7 = 343 - 252 = 91. (x, y = 3, 4.)

Answer: A) 91

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