Question

Найдите количество целых корней уравнения |x^2-7x-8|:(x^2-7x-8)=|x^2+2x-8|:(-x^2-2x+8)

Answer 1

$x^2-7x-8 = 0, \ x_1=-1, x_2=8; \ x^2+2x-8=0, \ x_1=-4, x_2=2; \ \ x textless -4, \ x^2-7x-8 textgreater 0, x^2+2x-8 textgreater 0, \ (x^2-7x-8):(x^2-7x-8)=(x^2+2x-8):(-x^2-2x+8), \ 1=-1, \ 0cdot x = -2, \ xinvarnothing; \ \ -4 textless x textless -1, \ x^2-7x-8 textgreater 0, x^2+2x-8 textless 0, \ (x^2-7x-8):(x^2-7x-8)=-(x^2+2x-8):(-x^2-2x+8), \ 1=1, \ 0cdot x = 0, \ xin R, \ xin(-4;-1); \ \ -1 textless x textless 2, \ x^2-7x-8 textless 0, x^2+2x-8 textless 0, \ -(x^2-7x-8):(x^2-7x-8)=-(x^2+2x-8):(-x^2-2x+8), \ -1=1, \ 0cdot x = 2, \ xinvarnothing;$

$2 textless x textless 8, \ x^2-7x-8 textless 0, x^2+2x-8 textgreater 0, \ -(x^2-7x-8):(x^2-7x-8)=(x^2+2x-8):(-x^2-2x+8), \ -1=-1, \ 0cdot x = 0, \ xin R; \ xin(2;8); \ \ x textgreater 8, \ x^2-7x-8 textgreater 0, x^2+2x-8 textgreater 0, \ (x^2-7x-8):(x^2-7x-8)=(x^2+2x-8):(-x^2-2x+8), \ 1=-1, \ 0cdot x = -2, \ xinvarnothing; \ \ xin(-4;-1)cup(2;8); \ X_Z={-3, -2, 3, 4, 5, 6, 7}, \ 7.$