Solve the problem.
-The sum of the squares of two numbers is 5. The difference of the two numbers is 1. Find the two numbers.
A) -2 and -1
B) -2 and -1; or 1 and 2
C) -2 and 1; or -1 and 2
D) 1 and 2

Question

Quizplus · Accepted Answer

Let the two numbers be x and y. Then, x^2 + y^2 = 5 and x - y = 1. Squaring both sides of x - y = 1, we get x^2 - 2xy + y^2 = 1. Substituting x^2 + y^2 = 5 into this equation, we get -2xy = 4. Therefore, xy = -2. Substituting this into x^2 + y^2 = 5, we get x^2 + y^2 = 5 - 2xy = 5 - 2(-2) = 9. Therefore, x^2 = 4 and y^2 = 5. Therefore, x = 2 or x = -2, and y = 1 or y = -1. Therefore, the two numbers are -2 and -1, or 1 and 2.

Solve the Problem. -The Sum of the Squares of Two Numbers Is 5