Đáp án:
Giải thích các bước giải:
(x ²-8x) ²+7(4-x)²=256
⇔(x ²-8x) ²+7(x²-8x+16)-256=0
⇔(x ²-8x) ²+7(x²-8x)-144=0
đặt x²-8x=a(a≥-16),pt trở thành:
a²+7a-144=0
⇔(a-9)(a+16)=0
⇔\(\left[ \begin{array}{l}a-9=0\\a+16=0\end{array} \right.\)⇔\(\left[ \begin{array}{l}a=9(n)\\a=-16(n)\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x^{2}-8x=9\\x^{2}-8x=-16\end{array} \right.\)⇔\(\left[ \begin{array}{l}x^{2}-8x-9=0\\x^{2}-8x+16=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}(x-9)(x+1)=0\\(x-4)^{2}=0\end{array} \right.\)⇔\(\left[ \begin{array}{l}\left[ \begin{array}{l}x-9=0\\x+1=0\end{array} \right.\ \\x-4=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}\left[ \begin{array}{l}x=9\\x=-1\end{array} \right.\ \\x=4\end{array} \right.\)
vậy:S={-1;4;9}
