Question

Уравнение у виду x^n=a и решите его 1) 1\8x=1 2) 1000x^3+1=0 3)1\27x^3=0,001 4)1\9x^4-16=0 5)1+x^5=0 6) x^8-16=0

Answer 1

1.
$\frac{1}{8}x^3=1 \\x^3=8\\x^3=2^3\\ x=2$
2.
$1000x^3+1=0 \\ 1000x^3=-1\\x^3=- \frac{1}{1000} \\x^3=-( \frac{1}{10})^3\\x=0,1$
3.
$\frac{1}{27} x^3=0,001 \\ x^3=0,027 \\x^3=(0,3)^3\\x=0,3$
4.
$\frac{1}{9} x^4-16=0 \\ \frac{1}{9}x^4=16\\x^4=9*16\\x= \sqrt[4]{3^2*2^4} \\|x|=2 \sqrt{3}\\ x_{1}=2 \sqrt{3}\\ x_{2} = -2\sqrt{3}$
5.
$1+x^5=0\\x^5=-1\\x^5=(-1)^5\\x=-1$
6.
$x^8-16=0 \\x^8=16\\x^8=2^4\\ x^2=2\\ x_{1} = \sqrt{2}\\ x_{2} = -\sqrt{2}$