Question

Решите уравнение 14x^2-14x-14=2x^2+x+13 4x^2-11x+4=2x^2+x+10

Answer 1

$14x^2-14x-14=2x^2+x+13$
$14x^2-14x-14-2x^2-x-13 = 0$
$12x^2-15x-27 = 0 |:3$
$4x^2-5x-9 = 0$
$D = 5^2 - 4*4*(-9) = 25+144 = 169 = 13^2$
$x_{1} = \frac{5+13}{2*4} = \frac{9}{4}$
$x_{2} = \frac{5-13}{2*4} = -1$

ответ: $-1; \frac{9}{4}$

$4x^2-11x+4=2x^2+x+10$
$4x^2-11x+4-2x^2-x-10 = 0$
$2x^2-12x-6 = 0 |:2$
$x^2-6x-3 = 0$
$D = 6^2 - 4*(-3) = 36+12 = 48 =( 4 \sqrt{3})^2$
$x_{1} = \frac{6+4 \sqrt{3}}{2} = 3+2 \sqrt{3}$
$x_{2} = \frac{6-4 \sqrt{3}}{2} = 3-2 \sqrt{3}$

ответ: $3-2 \sqrt{3} ; 3+2 \sqrt{3} .$