Question

Решить уравнение
$a) x^{3} -8x^{2}+15x=0 \\b) x^{4}-10 x^{2}+9=0$

Answer 1

$a) x^{3} -8 x^{2} +15x=0\\x( x^{2} -8x+15)=0\\x=0\\ x^{2} -8x+15=0\\D=64-60=4\\ \sqrt{D} =2\\ x_{1} = \frac{2+4}{2} = \frac{6}{2} =3\\ x_{2} = \frac{2-4}{2} =-1$

$b) x^{4} -10 x^{2} +9=0\\ x^{2} =t\\ x^{4} =t ^{2} \\ \\ t ^{2} -10t+9=0\\D=100-36=64\\ \sqrt{D} =8\\ x_{1} = \frac{10+8}{2} =9\\ x_{2} = \frac{10-8}{2} =1 \\ x^{2} =9\\x=+-3\\ x^{2} =1\\x=+-1$