Question

1. Rezolvați ecuația:
(2x² + 5x-4)²-5x²(2x² + 5x-4) + 6x^4= 0.

Answer 1

Răspuns:

1; 4; ⅘

Explicație pas cu pas:

${(2 {x}^{2} + 5x - 4)}^{2} - 5 {x}^{2}(2 {x}^{2} + 5x - 4) + 6 {x}^{4} = 0$

$4 {x}^{4} + 25 {x}^{2} + 16 + 20 {x}^{3} - 16 {x}^{2} - 40x - 10 {x}^{4} - 25 {x}^{3} + 20 {x}^{2} + 6 {x}^{4} = 0$

$- 5 {x}^{3} + 29 {x}^{2} - 40x + 16 = 0$

$5 {x}^{3} - 29 {x}^{2} + 40x - 16 = 0$

$(x - 1)(5 {x}^{2} - 24x + 16) = 0$

$\Delta = 24^{2} - 4 \cdot 5 \cdot 16 = 256 = 16^{2}$

$x_{2,3} = \frac{24 \pm 16}{10}$

$(x - 1)(x - 4)(5x - 4) = 0$

$x - 1 = 0 \implies \bf x = 1$

$x - 4 = 0 \implies \bf x = 4$

$5x - 4 = 0 \implies \bf x = \frac{4}{5}$