Question

(x-3) (x^{2} +3x+9)-x(x-4)(x+4)>21 Решите неравенство

Answer 1

$\displaystyle\bf\\\underbrace{(x-3)(x^{2} +3x+9)}_{x^{3} -3^{3}}-x\cdot\underbrace{(x-4)(x+4) }_{x^{2} -4^{2} } > 21\\\\\\x^{3} -3^{3} -x\cdot(x^{2} -4^{2}) > 21\\\\\\x^{3} -27-x\cdot(x^{2} -16) > 21\\\\\\x^{3} -27-x^{3} +16x > 21\\\\\\16x > 21+27\\\\\\16x > 48\\\\\\x > 3\\\\\\Otvet:x\in\Big(3 \ ; \ +\infty\Big)$