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Numbers $x$ and $y (x > y)$ have sum 15 and product 54. Compute $x^{2} - y^{2}$ .

Competition practiceAlgebra

A45
B117
C225
D27

Step-by-Step Solution

(x - y)^{2} = 225 - 216 = 9

, so

x - y = 3

and

x^{2} - y^{2} = (x + y) (x - y) = 15 \times 3 = 45

.

Answer: A) 45

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