Question

x^2=x^3+2x^4
21 задание огэ.
квадратное неравенство​

Answer 1

${x}^{2} = {x}^{3} + 2x^{4}$

${x}^{2} - {x}^{3} - 2 {x}^{4} = 0$

${x}^{2} \times (1 - x - 2 {x}^{2} ) = 0$

${x}^{2} \times ( - 2 {x}^{2} - x + 1) = 0$

${x}^{2} \times ( - 2 {x}^{2} + x - 2x + 1) = 0$

${x}^{2} \times ( - (2x - 1) \times (x + 1)) = 0$

$- {x}^{2} \times (2x - 1) \times (x + 1) = 0$

$- {x}^{2} = 0 \: \: \: \: \: \: 2x - 1 = 0 \: \: \: \: \: \: x + 1 = 0$

$x = 0 \: \: \: \: \: \: x = \frac{1}{2} \: \: \: \: \: \: x = - 1$