Question

Добрый вечер решите не равенство

Answer 1

$x-7+ \frac{(x-6)^2}{3} \geq \frac{(x+4)^2}{2} - \frac{(x+2)(x+6)}{4}$
$\frac{3(x-7)+(x-6)^2}{3} \geq \frac{2(x+4)^2}{4} - \frac{(x+2)(x+6)}{4}$
$\frac{3x-21+x^2-12x+36}{3} \geq \frac{2(x^2+8x+16)}{4} - \frac{ x^{2} +2x+6x+12}{4}$
$\frac{x^2-9x+15}{3} \geq \frac{2x^2+16x+32-x^2-8x-12}{4}$
$\frac{x^2-9x+15}{3} \geq \frac{x^2+8x+20}{4}$
$4(x^2-9x+15) \geq {3(x^2+8x+20)$
$4x^2-36x+60 \geq {3x^2+24x+60$
$4x^2-36x+60 -{3x^2-24x-60 \geq 0$
$x^2-60x \geq 0$
$x(x-60) \geq 0$
$x=0$    $x=60$

-----+------[0]---------_--------[60]------+-------
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Ответ: $(-$ ∞ $;0]$ ∪ $[60;+$ ∞ $)$