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