Question

Решите неравенство ((x^4-3x^2)(x^4+x^3-8x-8))/((x+2)(1-x)) меньше нуля.

Answer 1

$frac{(x^4-3x^2)(x^4+x^3-8x-8)}{(x+2)(1-x)} textless 0\\ frac{x^2(x^2-3)cdot ((x^3(x+1)-8(x+1))}{-(x+2)(x-1)} textless 0\\ frac{x^2(x-sqrt3)(x+sqrt3)(x+1)(x^3-8)}{(x+2)(x-1)} textgreater 0\\ frac{x^2(x-sqrt3)(x+sqrt3)(x+1)(x-2)(x^2+2x+4)}{(x+2)(x-1)}>0; ,; xne -2;xne 1\\x^2 geq 0; ,; ; x^2+2x+4 textgreater 0; ; pri; ; xin (-infty ,+infty )\\+++(-2)---(-sqrt3)+++(-1)---(1)+++(sqrt3)---(, 2, )+++\\xin (-infty ,-2)cup (-sqrt3,-1)cup (1,sqrt3)cup (2,+infty )$