Question

If x + y = 11 and xy = 30 then x² + y² is equal to ______.

Options

• 61

• 56

• 58

• 65

Answer 1

If x + y = 11 and xy = 30 then x² + y² is equal to 61.

Explanation:

Given: x + y = 11 and xy = 30.

We want to find x² + y².

Using the identity: (x + y)² = x² + y² + 2xy

Substitute the given values:

11² = x² + y² + 2(30) 

121 = x² + y² + 60

Solve for x² + y²:

x² + y² = 121 – 60

x² + y² = 61

Hence, x² + y² = 61.