Question

The sum of the squares of two consecutive real numbers is 61. Find the numbers.

Answer 1

• Answer:

1. (5 ; 6)

2. (-5 ; -6)

• Step-by-step explanation:

consecutive numbers => x ; (x + 1)

x² + (x + 1)² = 61

x² + x² + 2x + 1 = 61

2x² + 2x + 1 - 61 = 0

2x² + 2x - 60 = 0 | : 2

x² + x - 30 = 0

x = $\frac{-1+/-\sqrt{1^{2}-4*1*-30}}{2*1}$

x = $\frac{-1+/-\sqrt{121}}{2}$

x = $\frac{-1+/-11}{2}$

x₁ = $\frac{-1+11}{2}=\frac{10}{2}=5$

x₂ = $\frac{-1-11}{2}=\frac{-12}{2}=-6$

Solutions

1. (5 ; 6)

5² + 6² = 25 + 36 = 61

2. (-5 ; -6)

(-5)² + (-6)² = 25 + 36 = 61