Question

решите неравенство
-10/х^2-4х-5 ≤ 0

Answer 1

Ответ: x ∈ ( -∞ ; -1 ) ∪ (5 ; ∞)

Объяснение:

$\displaystyle \large \boldsymbol {} \frac{-10}{x^2-4x-5} \leq 0 \ \ \ | \times -1 \\\\\\ \frac{10}{x^2-4x-5} \geq 0 \\\\\\ x^2-4x-5=0 \\\\\\\left \{ {{x_1+x_2=4} \atop {x_1x_2=-5}} \right. => x_1=5 \ \ ; \ \ x_2=-1 \\\\\\ (x+1)(x-5)> 0 \\\\\\ znaki: +++(-1)---(5)+++$

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$\large \boldsymbol {x \in (-\infty \ ; \ -1 ) \ \cup \ (5 \ ; \ \infty ) }$