Question

[Đào Trí Bình]

(4x - 1)² = (1 - 4x)⁴

Gíup mình tìm x nha mn

Answer 1

[『Kuroba ム Tsuki Ryoo ︵²ᵏ⁷』]

`@` `\text {Ans}`

`\downarrow`

`(4x - 1)^2 = (1 - 4x)^4`

`\Rightarrow (4x - 1)^2 - (1 - 4x)^4 = 0`

`\Rightarrow (4x - 1)^2 - (4x - 1)^4 = 0`

`\Rightarrow (4x - 1)^2. [1 - (4x - 1)^2] = 0`

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

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

`\Rightarrow`\(\left[{}\begin{matrix}4x=1\\4x-1=1\\4x-1=-1\end{matrix}\right.\)

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

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

Vậy, `x \in`\(\left\{0;\dfrac{1}{4};\dfrac{1}{2}\right\}\)