Question

Giải pt

\(\left(x-2\right)^4+\left(x-6\right)^4=82\)

Answer 1

Đặt x-4=t

x-2=t+2

x-6 = t - 2

pt <=> (t+2)⁴ + (t-2)⁴ = 82

<=> (t²+4+4t)² + (t²+4 -4t)² =82

<=> (t²+4)² +8t(t²+1)+16t² + (t²+4)² - 8t(t²+1)+16t² =82

<=> (t²+4)² + 16t² =41

<=> t⁴ + 24t² +16 -41 = 0 <=> \(\left[{}\begin{matrix}t^2=1\\t^2=-25\left(loai\right)\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}t=1\\t=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=5\end{matrix}\right.\)