Solve the problem using a system of equations: The sum of the squares of two numbers is 113. The difference of the numbers is 1. Find the numbers.

Question



Answer 1

x^2 + y^2 = 113

x -y = 1

y =x-1

x^2 +(x-1)^2 = 113

x^2 +x^2 -2x +1 = 113

2x^2 -2x -112 = 0

x^2 -x -56 = 0

(x-8)(x+7) = 0

x =-7 or 8

y= -8 or 7

difference of -8 and -7 is 1

difference of 8 and 7 is 1

8^2 +7^2 = 64+49 = 113

(-8)^2 + (-7)^2 = 64+ 49 = 113

the numbers are either 7 and 8, or -7 and -8