Question

Решите уравнение f(x-2)=f(x+1), если f(x)=4+2x-x^2

Answer 1

$f(x)=4+2x-x^2\\\\f(x-2)=4+2(x-2)-(x-2)^2=\\=4+2x-4-(x^2-4x+4)=\\=2x-x^2+4x-4=6x-x^2-4\\\\f(x+1)=4+2(x+1)-(x+1)^2=\\=4+2x+2-(x^2+2x+1)=\\=6+2x-x^2-2x-1=5-x^2\\\\f(x-2)=f(x+1)\\6x-x^2-4=5-x^2\\6x=5+4\\6x=9\\x=1,5$