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suy ra3.(5x-1) - 4.(5x-1) + 6(5x-1) =15
suy ra 5.(5x-1) = 15
suy ra 5x-1=3
suy ra x=4/5
\(\Leftrightarrow3\left(5x-1\right)-4\left(5x-1\right)+6\left(5x-1\right)=15\)
\(\Leftrightarrow\left(3-4+6\right)\left(5x-1\right)=15\)
\(\Leftrightarrow5\left(5x-1\right)=15\)
\(\Leftrightarrow5x-1=\frac{15}{5}=3\)
\(\Leftrightarrow5x=3+1=4\)
\(\Leftrightarrow x=\frac{4}{5}\)
Vậy \(x=\frac{4}{5}\)
\(x^2=\frac{5}{7}x\)
\(=>x=\frac{5}{7}\)
Vậy pt trên có nghiệm là \(\frac{5}{7}\)
a, 5^x . (5^3)^2=625
5^x . 5^6=5^4
5^x=5^4:5^6
5^x=5^-2
=> x=-2
Bài 4.
\(\left|x-1\right|+\left|y-2\right|+\left(z-x\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}x-1=0\\y-2=0\\z-x=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=z=1\\y=2\end{cases}}\)
Bài 3.
\(\left|x-1\right|+\left|2x-2\right|+\left|4x-4\right|+\left|5x-5\right|=36\)
\(\Leftrightarrow\left|x-1\right|+2\left|x-1\right|+4\left|x-1\right|+5\left|x-1\right|=36\)
\(\Leftrightarrow12\left|x-1\right|=36\)
\(\Leftrightarrow\left|x-1\right|=3\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=3\\x-1=-3\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=4\\x=-2\end{cases}}\)
Ta có :
(x-1):2+1(số hạng)
=>(x+1)[(x-1):2+1]=72
(x+1)(x-1):2+(x+1)=72
(x+1)(x-1)+2(x+1)=72x2
(x+1)(x+1)=144
=> (x+1)( x+1)=12x12
=>x+1=12
=>x=11
Vậy x=11
\(1+3+5+...+x=36\)
\(\Rightarrow\frac{\left(x+1\right)\left[\left(x-1\right):2+1\right]}{2}=36\)
\(\Rightarrow\left(x+1\right)\left[\left(x-1\right):2+1\right]=36.2=72\)
\(\Rightarrow\left(x+1\right)\left(\frac{x-1}{2}+1\right)=72\)
\(\Rightarrow\left(x+1\right)\left(\frac{x-1}{2}+\frac{2}{2}\right)=72\)
\(\Rightarrow\left(x+1\right)\left(\frac{x+1}{2}\right)=72\)
\(\Rightarrow\left(\frac{x+1^2}{2}\right)=72\)
\(\Rightarrow\left(x+1\right)^2=144\)
\(\Rightarrow\left(x+1\right)^2=12^2\)
\(\Rightarrow x+1=12\)
\(\Rightarrow x=12-1=11\)