Question

tìm x biết:

a.2x+3=(3+2x)²

^{b.(x-5)^2=5-x}

^c.(x+2)³=(x+2)

d.|3x-1|=(1-3x)²

e.2x(x+3).(3-x)+(x+1).(x-1)=7

mn làm nhanh mih tik nha

Answer 1

a)

\(2x+3=(2x+3)^2\)

\(\Leftrightarrow (2x+3)^2-(2x+3)=0\)

\(\Leftrightarrow (2x+3)(2x+3-1)=0\)

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

b) \((x-5)^2=5-x\)

\(\Leftrightarrow (x-5)^2+(x-5)=0\)

\(\Leftrightarrow (x-5)(x-5+1)=0\)

\(\Leftrightarrow (x-5)(x-4)=0\)

\(\Rightarrow \left[\begin{matrix} x-5=0\\ x-4=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=5\\ x=4\end{matrix}\right.\)

c) \((x+2)^3=x+2\)

\(\Leftrightarrow (x+2)^3-(x+2)=0\)

\(\Leftrightarrow (x+2)[(x+2)^2-1]=0\)

\(\Leftrightarrow (x+2)(x+2-1)(x+2+1)=0\)

\(\Leftrightarrow (x+2)(x+1)(x+3)=0\)

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

Answer 2

d)

\(|3x-1|=(1-3x)^2\)

\(\Leftrightarrow |3x-1|=|3x-1|^2\)

\(\Leftrightarrow |3x-1|^2-|3x-1|=0\)

\(\Leftrightarrow |3x-1|(|3x-1|-1)=0\)

\(\Rightarrow \left[\begin{matrix} |3x-1|=0\\ |3x-1|-1=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} |3x-1|=0\\ |3x-1|=1\end{matrix}\right.\)

\(\Rightarrow \left[\begin{matrix} 3x-1=0\\ 3x-1=\pm 1\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=\frac{1}{3}\\ x=\frac{2}{3}\\ x=0\end{matrix}\right.\)

e)

\(2x+(x+3)(3-x)+(x+1)(x-1)=7\)

\(\Leftrightarrow 2x+(3^2-x^2)+(x^2-1^2)=7\)

\(\Leftrightarrow 2x=-1\Rightarrow x=-\frac{1}{2}\)