Question

If x – y = 7 and xy = 9, find the value of (x² + y²).

Answer 1

x – y = 7 (given)

By squaring both the sides we get;

= (x – y)² = (7)² 

= x² + y² – 2xy = 49 

= x² + y² = 49 + 2xy 

Also given, 

xy = 9 

= x² + y² = 49 + 2(9) 

= x² + y² = 49 + 18 

= x² + y² = 67 

So, the value of x² + y² is 67.