Question

If x – y = 6 and xy = 27, find the value of x² + y².

Answer 1

Given: x – y = 6 and xy = 27

Step 1: Use the identity for the square of a difference:

(x – y)² = x² – 2xy + y²

Step 2: Substitute the given values:

6² = x² – 2(27) + y² 

36 = x² – 54 + y²

Step 3: Rearrange to find (x² + y²): 

x² + y² = 36 + 54

x² + y² = 90