Question

решить неравенство:
$frac{15}{4+3x-x^2} textgreater 1$

Answer 1

$frac{15}{4+3x-x^2} textgreater 1\\ frac{15}{4+3x-x^2} -1 textgreater 0\\ frac{15-4-3x+x^2}{-(x^2-3x-4)} textgreater 0\\ frac{x^2-3x+11}{x^2-3x-4} textless 0\\x^2-3x-4=0; ; Rightarrow ; ; x_1=-1,; x_2=4; ; (teorema; Vieta)\\x^2-3x+11=0; ,; ; D=9-44=-35 textless 0; ; Rightarrow ; ; x^2-3x+11 textgreater 0\\Rightarrow ; ; x^2-3x-4 textless 0\\(x+1)(x-4) textless 0quad quad +++(-1)---(4)+++\\xin (-1,4)$