Question

The sum of the squares of two positive numbers is 109. The difference of their squares is 91. Find the two

numbers.

Answer 1

3 and 10

Explanation:

x² + y² = 109

x² - y² = 91

Add the equations

2x² = 200

x² = 100

x = 10

Substitute x² = 100 into either equation

100 - y² = 91

y² = 9

y = 3