Question

Tìm x

(4x+5)¹⁰⁰= (4x+5)¹⁰²

Answer 1

Theo giả thiết, ta có:

\(\left(4x+5\right)^{100}=\left(4x+5\right)^{102}\\ =>\left[{}\begin{matrix}4x+5=0\\4x+5=1\\4x+5=-1\end{matrix}\right.< =>\left[{}\begin{matrix}x=-\dfrac{5}{4}\\x=-1\\x=-\dfrac{3}{2}\end{matrix}\right.\)

Vậy: \(x\in\left\{-\dfrac{5}{4};-\dfrac{3}{2};-1\right\}\)

Answer 2

Theo đề bài, ta có:

\(\left(4x+5\right)^{100}=\left(4x+5\right)^{102}=\left[{}\begin{matrix}0\\1\\-1\end{matrix}\right.\)

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

Vậy, \(x\in\left\{\dfrac{-5}{4};-1;\dfrac{-3}{2}\right\}\).