Question

The number x is 2 more than the number y. If the sum of the squares of x and y is 34, then find the product of x and y.

Answer 1

Given x is 2 more than y, so x = y + 2
Sum of squares of x and y is 34, so x² + y² = 34.
Replace x = y + 2 in the above equation and solve for y.
We get (y + 2)² + y² = 34

2y² + 4y - 30 = 0
y² + 2y - 15 = 0
(y + 5)(y - 3) = 0
So y = -5 or 3
For y = -5, x =-3
For y = 3, x = 5
Product of x and y is 15 in both cases.