The difference of two numbers is 3 and the sum of their squares is 29 . Find the numbers.

Answer 1

Two unknowns (A and B), so we need two formulas.

A - B = 3

A²+ B² = 25.

The formulas are in different forms, so use substitution.

(B+3)² + B² = 29

B² + 3b + 3b + 9 + B² = 29 = 2B² + 6b + 9 = 29

Set equal to 0 to solve: = 2B² + 6b -20 = 0

factor out a 2. 2(B² + 3b - 10)

C is negative, so the factors are opposite signs.

2(b+5) (b-2) Let's take the positive solution b= 2 A -B = 3. so A = 5

Answer 2

Hi Kendal,

The two numbers you are looking for are 2 and 5.

2 squared = 4

5 squared = 25.

4 + 25 = 29

5 - 2 = 3