Răspuns:
1; 4; ⅘
Explicație pas cu pas:
[tex]{(2 {x}^{2} + 5x - 4)}^{2} - 5 {x}^{2}(2 {x}^{2} + 5x - 4) + 6 {x}^{4} = 0 \\ [/tex]
[tex]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[/tex]
[tex] - 5 {x}^{3} + 29 {x}^{2} - 40x + 16 = 0 [/tex]
[tex]5 {x}^{3} - 29 {x}^{2} + 40x - 16 = 0[/tex]
[tex](x - 1)(5 {x}^{2} - 24x + 16) = 0[/tex]
[tex]\Delta = 24^{2} - 4 \cdot 5 \cdot 16 = 256 = 16^{2}[/tex]
[tex]x_{2,3} = \frac{24 \pm 16}{10} \\[/tex]
[tex](x - 1)(x - 4)(5x - 4) = 0[/tex]
[tex]x - 1 = 0 \implies \bf x = 1[/tex]
[tex]x - 4 = 0 \implies \bf x = 4[/tex]
[tex]5x - 4 = 0 \implies \bf x = \frac{4}{5} \\ [/tex]
