Question

Розвязати рівняння (х-3)⁴ + (х²-6х)+7=0

Answer 1

(x²-6x+9)²+(x²-6x+9)-2=0
(x-3)²=a
a²+a-2=0
A1+a2=-1 U a1*a2=-2
a1=-2⇒(x-3)²=-2 нет решения
a2=1⇒(x-3)²=1
x-3=-1 U x-3=1
x=2 U x=4

Answer 2

$(x-3)^4+(x^2-6x)+7=0 \\ (x-3)^4+(x-3)^2-9+7=0 \\ z=x-3 \\ z^4+z^2-2=0 \\ m=z^2 \geq 0 \\ m^2+m-2=0 \\ D=b^2-4ac=1-4(-2)=1+8=9\ \textgreater \ 0 \\ m_1= \frac{-b- \sqrt{D} }{2a}= \frac{-1-3}{2}=-2\ \textless \ 0 \\ m_2= \frac{-b+ \sqrt{D} }{2a} = \frac{-1+3}{2}=1\ \textgreater \ 0 \\ z^2=1;z^2-1=0;(z-1)(z+1)=0;z_1=-1;z_2=1 \\ x_1-3=-1;x_1=3-1=2 \\ x_2-3=1;x_2=3+1=4$