Question

giải các phương trình:
a)\(\left(x+3\right)^4+\left(x+5\right)^4=16\)

b)\(\left(x-2\right)^4+\left(x-3\right)^4=1\)

c)\(\left(x+1\right)^4+\left(x-3\right)^4=82\)

d)\(\left(x-2,5\right)^4+\left(x-1,5\right)^4=1\)

Answer 1

a) (x+3)⁴+(x+5)⁴=16

<=>(x+3)⁴+(x+5)⁴=0⁴+2⁴

TH1: \(\left\{{}\begin{matrix}x+3=0\\x+5=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\\x=-3\end{matrix}\right.\Leftrightarrow x=-3\)

TH2:\(\left\{{}\begin{matrix}x+3=2\\x+5=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1\\x=-5\end{matrix}\right.\)(loại)

b)(x-2)⁴+(x-3)⁴=1=0⁴+1⁴

TH1: \(\left\{{}\begin{matrix}x-2=0\\x-3=1\end{matrix}\right.\)loại

TH2: \(\left\{{}\begin{matrix}x-2=1\\x-3=0\end{matrix}\right.\)=>x=3.

c)(x+1)⁴+(x-3)⁴=82=3⁴+(-1)⁴

làm tương tự => x=2.

d) làm tương tự câu b