Verified answer

Ответ:

...........

Объяснение:

а)

[tex]3 {x}^{2} + 7x - 6 = 0 \\ a = 3\\ b = 7 \\ c = - 6\\ D = {b}^{2} - 4ac = {7}^{2} - 4 \times 3 \times ( - 6) = 49 + 72 = 121 \\ x_{1} = \frac{ - 7 - 11}{2 \times 3} = - \frac{18}{6} = - 3 \\ x_{2} = \frac{ - 7 + 11}{2 \times 3} = \frac{4}{6} = \frac{2}{3} [/tex]

б)

[tex] {x}^{4} - 5 {x}^{2} + 4 = 0 \\ {x}^{2} = a, \: \: a \geqslant 0 \\ {a}^{2} - 5a + 4 = 0[/tex]

По теореме Виета

[tex] {x}^{2} + bx + c = 0\\ x_{1} + x_{2} = - b\\ x_{1} x_{2} = c [/tex]

[tex]a_{1} + a _{2}= 5 \\ a_{1}a _{2}= 4 \\ a_{1} =4 \\ a _{2}= 1[/tex]

[tex] {x}^{2} = 4 \\ {x}^{2} = 1 \\ \\ x_{1} = - 2 \\ x_{2} = 2\\ x_{3} = - 1 \\ x_{4} = 1[/tex]