Question

[Nguyễn Khánh Linh]

giúp m với mn

(3/5.x-2)⁴ =16/81

Answer 1

[⭐Hannie⭐]

`(3/5 x-2)^4 =16/81`

`=> (3/5 x-2)^4 =(+-2/3)^4`

\(\Rightarrow\left[{}\begin{matrix}\dfrac{3}{5}x-2=\dfrac{2}{3}\\\dfrac{3}{5}x-2=-\dfrac{2}{3}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}\dfrac{3}{5}x=\dfrac{8}{3}\\\dfrac{3}{5}x=\dfrac{4}{3}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{40}{9}\\x=\dfrac{20}{9}\end{matrix}\right.\)

Answer 2

[HT.Phong (9A5)]

\(\left(\dfrac{3}{5}x-2\right)^4=\dfrac{16}{81}\)

\(\Rightarrow\left[\left(\dfrac{3}{5}x-2\right)^2\right]^2=\left(\dfrac{4}{9}\right)^2\)

TH1: \(\left(\dfrac{3}{5}x-2\right)^2=-\dfrac{4}{9}\) (vô lý) 

Vì: \(\left(\dfrac{3}{5}x-2\right)^2\ge0\forall x\) mà \(-\dfrac{4}{9}< 0\)

TH2: \(\left(\dfrac{3}{5}x-2\right)^2=\dfrac{4}{9}\)

\(\Rightarrow\left(\dfrac{3}{5}x-2\right)^2=\left(\dfrac{2}{3}\right)^2\)

Ta lại có hai trương hợp: 

TH1: \(\dfrac{3}{5}x-2=\dfrac{2}{3}\)

\(\Rightarrow\dfrac{3}{5}x=\dfrac{8}{3}\Rightarrow x=\dfrac{40}{9}\) 

TH2: \(\dfrac{3}{5}x-2=-\dfrac{2}{3}\)

\(\Rightarrow\dfrac{3}{5}x=\dfrac{4}{3}\Rightarrow x=\dfrac{20}{9}\)