Question

Tìm x

\(\left(x-3\right)^{x+5}-\left(x-3\right)^{x+15}=0\)

Answer 1

\(\Leftrightarrow\left(x-3\right)^{x+5}\left(1-\left(x-3\right)^{10}\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-3\right)^{x-5}=0\\\left(x-3\right)^{10}=1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x-3=0\\x-3=1\\x-3=-1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=3\\x=4\\x=2\end{matrix}\right.\)

Answer 2

Ta có:

(x-3)^x+5-(x-3)^x+15=0

<=> (x-3)^x+5*(1-(x-3)¹⁰)=0

=> (x-3)^x-5=0->x-3=0->x=3

(x-3)¹⁰=1->x-3=1 và x-3=-1

->x=4 và x=2

Vậy x=3, x=4 và x=2