Question

Tìm x biết:

\(\text{(2x+1)}^4\) = \(\text{(2x+1)}^6\)

Answer 1

\(\left(2x+1\right)^4=\left(2x+1\right)^6\)

\(\Rightarrow\left(2x+1\right)^6-\left(2x+1\right)^4=0\)

\(\Rightarrow\left(2x+1\right)^4.\left[\left(2x+1\right)^2-1\right]=0\)

\(\Rightarrow\left(2x+1\right)^4=0\) hoặc \(\left(2x+1\right)^2-1=0\)

+) \(\left(2x+1\right)^4=0\Rightarrow2x+1=0\Rightarrow x=-0,5\)

+) \(\left(2x+1\right)^2-1=0\Rightarrow\left(2x+1\right)^2=1\)

\(\Rightarrow2x+1=\pm1\)

+ \(2x+1=1\Rightarrow x=0\)

+ \(2x+1=-1\Rightarrow x=-1\)

Vậy \(x\in\left\{-0,5;0;-1\right\}\)

Answer 2

(2x+1)⁴=(2x+1)⁶

\(\Leftrightarrow\)16x+1=64x+1

\(\Leftrightarrow\)16x-64x=1-1

\(\Leftrightarrow\)-48x=0

\(\Leftrightarrow\)x=0

mik ko chắc..