Question

Question: If x² + y² = 36 and (x + y)² = 64, what is the value of xy?

Options:
A) 7
B) 14
C) 28
D) 100

Answer 1

By expanding the second equation (x + y)² and substituting from the first equation x² + y², we find that xy equals to 14, which is option B.

Step-by-step explanation:

You have been given two equations: x² + y² = 36 and (x + y)² = 64. To find the value of xy, we can expand the second equation and then compare it with the first one.

First, let's expand (x + y)²:

(x + y)² = x² + 2xy + y²

Now we can substitute the given value from the first equation (x² + y² = 36) into the second:

64 = 36 + 2xy

Next, we subtract 36 from both sides to solve for 2xy:

2xy = 64 - 36

2xy = 28

Divide both sides by 2 to find xy:

xy = ⅔ × 28

xy = 14

Therefore, the value of xy is 14, which corresponds to option B.