IF `x^2+2xy+y^2=64` and y-x=12, which of the following could be the value of x?

Options

A. -10
B. -4
C. 2
D. 10

Answer

To solve the problem, we are given two equations:

1. \( x^2 + 2xy + y^2 = 64 \)
2. \( y - x = 12 \)

We will solve these equations step by step.

### Step 1: Rewrite the first equation

The first equation can be rewritten using the identity \( (x + y)^2 = x^2 + 2xy + y^2 \):

\[ (x + y)^2 = 64 \]