If x2 + 2xy + y2 = 64 and y - x = 12, which of the following could be the value of x ?
A. -10
B. -4
C. 2
D. 10
Answer:A
If x2 + 2xy + y2 = 64 and y - x = 12, which of the following could be the value of x ?
A. -10 B. -4 C. 2 D. 10
Explanation: A Factoring the left side of the equation x2 + 2xy + y2 = 64 gives (x + y)2 = 64. Taking the square root of both sides of the equation, we find that x + y = 8 or -8. The other equation provides that y - x = 12, so y = x + 12 . Substitute this value of y into the first equation: either x + (x + 12) = 8, so 2x + 12 = 8, 2x = -4, and x = -2, or else or x + (x + 12) = -8, so 2x + 12 = -8, so 2x = -20, and x = -10. Therefore, x could be either -2 or -10, and only -10 is an option in the answers, so (A) is correct.