Question

Решите уравнение f(x+2)=f(x-2), если f(x)=x^2-x+5

Answer 1

$f(x+2)=(x+2)^2-(x+2)+5 = x^2+4x+4-x-2+5 = \\ = x^2-3x+7 \\ \\ f(x-2)=(x-2)^2-(x-2)+5=x^2-4x+4-x+2+5 = \\ = x^2-5x+7 \\ \\ x^2-3x+7=x^2-5x+7 \\ -3x=-5x \\ -3x+5x=0 \\ 2x=0 \\ x = 0$