1. (5 ; 6)
2. (-5 ; -6)
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 = [tex]\frac{-1+/-\sqrt{1^{2}-4*1*-30}}{2*1}[/tex]
x = [tex]\frac{-1+/-\sqrt{121}}{2}[/tex]
x = [tex]\frac{-1+/-11}{2}[/tex]
x₁ = [tex]\frac{-1+11}{2}=\frac{10}{2}=5[/tex]
x₂ = [tex]\frac{-1-11}{2}=\frac{-12}{2}=-6[/tex]
Solutions
1. (5 ; 6)
5² + 6² = 25 + 36 = 61
2. (-5 ; -6)
(-5)² + (-6)² = 25 + 36 = 61
