Question

55 баллов (2x4 − 34)·(3 − x) = 2·(x − 3). 55 балов

Answer 1

Ответ: x₁ =-3 ; x₂ = 2 ;  x₃ = -2

Объяснение:

$\sf \displaystyle (2x^4-34)(3-x)=2(x-3)~~ ; ~~\boxed{ \boldsymbol {\sf x-3=-(3-x)}} \\\\\\ (2x^4-34)(3-x)=-2(3-x) \\\\ (2x^4-34)(3-x)+2(3-x) =0 \\\\ (x-3)(2x^4-34+2)=0 \\\\ (x-3)(2x^4-32)=0 \\\\ 2(x-3)(x^4-16)=0 \\\\2(x-3) (x^2-4)(x^2+4) =0$


$\sf \hspace{-1em}1) ~ x-3=0 \\\\ x_1=3~~ \checkmark$

$\hspace{-1,3em}2) ~ \sf x^2-4=0 \\\\ \sf x^2=4 \\\\ x_{2,3}=\pm 2 ~~\checkmark$


$\hspace{-1,3em}3) ~ \sf x^2+4=0 \\\\ \sf x^2=-4 ~~ \varnothing$