Question

If x + y = 7 and x – y = 2, find the value of x² + y².

Answer 1

Given: x + y = 7 and x – y = 2

Step-wise calculation:

1. From the identity,

(x + y)² = x² + y² + 2xy 

So, x² + y² = (x + y)² – 2xy

2. Also, (x – y)² = x² + y² – 2xy

3. Adding the two equations,

(x + y)² + (x – y)² = 2(x² + y²)

4. Substitute given values,

7² + 2² = 2(x² + y²) 

49 + 4 = 2(x² + y²)

53 = 2(x² + y²)

5. Divide both sides by 2,

x² + y² = `53/2`