[tex]a)5x {}^{3} + 2 = x {}^{2} + 10x [/tex]
[tex]5x {}^{3} + 2 - x {}^{2} - 10x = 0[/tex]
[tex]x {}^{2} \times (5x - 1) - 2( - 1 + 5x) = 0[/tex]
[tex](5x - 1) \times (x {}^{2} - 2) = 0[/tex]
[tex]5x - 1 = 0 \\ x {}^{2} - 2 = 0[/tex]
[tex]x = \frac{1}{5} \\ x = - \sqrt{ 2} \\ x = \sqrt{2} [/tex]
Działanie ma trzy rozwiązania :
[tex]x _{1} = - \sqrt{2} \: \: \: x _{2} = \frac{1}{5} \: \: \: x _{3} = \sqrt{2} [/tex]
[tex]x {}^{5} - 6x {}^{4} = 7x {}^{3} [/tex]
[tex]x {}^{5} - 6x {}^{4} - 7 {x}^{3} = 0[/tex]
[tex]x {}^{3} \times (x {}^{2} - 6x - 7) = 0[/tex]
[tex]x {}^{3} \times (x {}^{2} + x - 7x - 7) = 0[/tex]
[tex]x {}^{3} \times (x \times (x + 1) - 7(x + 1)) = 0 \\ [/tex]
[tex]x {}^{3} \times (x + 1) \times (x - 7) = 0[/tex]
[tex]x {}^{3} = 0 \\ x + 1 = 0 \\ x - 7 = 0[/tex]
[tex]x = 0 \\ x = - 1 \\ x = 7[/tex]
Działanie ma trzy rozwiązania :
[tex]x _{1} = - 1 \: \: \: \: x _{2} = 0 \: \: \: \: x _{3} = 7[/tex]