tìm x
( x+1)\(^{x+1}\)=(x+1)\(^{x+3}\)
giúp với
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\(2x\left(x+3\right)-3\left(x^2+1\right)=x+1-x\left(x-2\right)\)
\(\Leftrightarrow2x^2+6x-3x^2-3=x+1-x^2+2x\)
\(\Leftrightarrow-x^2+6x-3=-x^2+3x+1\)
\(\Leftrightarrow3x=4\)
hay \(x=\dfrac{4}{3}\)
\(2x\left(x+3\right)-3\left(x^2+1\right)=x+1-x\left(x-2\right)\)
\(\Leftrightarrow2x^2+6x-3x^2-3=x+1-x^2+2x\)
\(\Leftrightarrow3x=4\Leftrightarrow x=\dfrac{4}{3}\)
\(\left(x+1\right)^3-\left(x-1\right)\left(x^2+x+1\right)-2=0\)
\(\Rightarrow x^3+3x^2+3x+1-x^3+1-2=0\)
\(\Rightarrow3x^2+3x=0\Rightarrow3x\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
\(3^{x-1}+3^{x+1}-1=89\)
\(3^{x-1}.\left(1+3^2\right)=89+1\)
\(3^{x-1}.10=90\)
\(3^{x-1}=90:10\)
\(3^{x-1}=9\)
\(3^{x-1}=3^2\)
\(x-1=2\)
\(x=2+1\)
\(x=3\)
\(3^{x-1}+3^{x+1}-1=89\)
\(\Rightarrow3^x\cdot\left(3^{-1}+3^1\right)=89+1\)
\(\Rightarrow3^x\cdot\left(\dfrac{1}{3}+3\right)=90\)
\(\Rightarrow3^x\cdot\dfrac{10}{3}=90\)
\(\Rightarrow3^x=90:\dfrac{10}{3}\)
\(\Rightarrow3^x=27\)
\(\Rightarrow3^x=3^3\)
\(\Rightarrow x=3\)
\(a,\Leftrightarrow x^3-8-x\left(x^2-9\right)=1\\ \Leftrightarrow x^3-8-x^3+9x=1\\ \Leftrightarrow9x=9\Leftrightarrow x=1\\ b,\Leftrightarrow8x^3+12x^2+6x+1-8x^3 +12x^2-6x+1-24x^2+24x-1=0\Leftrightarrow1=0\Leftrightarrow x\in\varnothing\)
a) \(\Leftrightarrow x^3-8-x^3+9x=1\)
\(\Leftrightarrow9x=9\Leftrightarrow x=1\)
b) \(\Leftrightarrow8x^3+12x^2+6x+1-8x^3+12x^2-6x+1-24x^2+24x-6=5\)
\(\Leftrightarrow24x=9\Leftrightarrow x=\dfrac{3}{8}\)
Bài 2:
a: =>x=0 hoặc x=-3
b: =>x-2=0 hoặc 5-x=0
=>x=2 hoặc x=5
c: =>x-1=0
hay x=1
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\(\left(x+1\right)^{x+3}=\left(x+1\right)^{x+1}\)
\(\Leftrightarrow\left(x+1\right)^{x+1}\cdot x\cdot\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=0\\x=-2\end{matrix}\right.\)