a. \(pt\) ⇔ \(\left(x-5\right)^4+\left(x-2\right)^4=17\)
Đặt \(t=x\) \(-\dfrac{5+2}{2}\) \(=\) \(x-\dfrac{7}{2}\)
\(pt\) trở thành: \(\left(t+\dfrac{7}{2}-5\right)^4+\left(x+\dfrac{7}{2}-2\right)^4=17\)
⇔ \(\left(t-\dfrac{3}{2}\right)^4+\left(t+\dfrac{3}{2}\right)^4=17\)
⇔ \(\left(2t^2+\dfrac{9}{2}\right)^2-2\left(t^2-\dfrac{9}{4}\right)^2\) \(=17\)
⇔ \(2t^4+27t^2-\dfrac{55}{8}=0\)
⇔ \(\left(t^4+2t^2.\dfrac{27}{4}+\dfrac{27^2}{4^2}\right)-\dfrac{27^2}{4^2}-\dfrac{55}{16}=0\)
⇔ \(\left(t^2+\dfrac{27}{4}\right)^2=49\)
\(\Leftrightarrow\left\{{}\begin{matrix}t^2=\dfrac{1}{4}\\\\t^2=-\dfrac{55}{4}\left(\times\right)\end{matrix}\right.\) \(\Rightarrow\) \(t=\pm\dfrac{1}{2}\)
Thay \(t=\pm\dfrac{1}{2}\) vào tự tính nha
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