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a) \(\left(x-\frac{1}{3}\right)^2-\frac{1}{4}=0\)
\(\Leftrightarrow\left(x-\frac{1}{3}\right)^2=\frac{1}{4}\)
\(\Leftrightarrow\left(x-\frac{1}{3}\right)^2=\left(\frac{1}{2}\right)^2\)
\(\Leftrightarrow\orbr{\begin{cases}x-\frac{1}{3}=\frac{1}{2}\\x-\frac{1}{3}=\frac{-1}{2}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{6}\\x=\frac{-1}{6}\end{cases}}}\)
Vậy x= 5/6 hoặc -1/6
b) - Nếu x=0 thì \(5^y=2^0+624=1+624=625=5^4\Rightarrow y=4\left(y\in N\right)\)
- Nếu x \(\ne\) 0 thì vế trái là số chẵn , vế phải là số lẻ \(\forall x;y\inℕ\) ( vô lí)
Vậy x=0, y=4
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1)3x+1.(33)x=35
3(x+1+3x)=35
\(\Rightarrow\)x+1+3x=5
4x+1=5
4x=5-1
4x=4
x=4:4
x=1 vậy x=1
![](https://rs.olm.vn/images/avt/0.png?1311)
(-2x-7)-(-5x+18)=35
=>-2x-7+5x-18=35
=>3x-25=35
=>3x=35+25
=>3x=60
=>x=60:3
=>x=20
(-2x-7)-(-5x+18)=35
-2x-7+5x-18=35
(-2x+5x)-(7+18)=35
3x-25=35
3x=35+25
3x=60
x=60:3
x=20
Vậy x=20
![](https://rs.olm.vn/images/avt/0.png?1311)
\(-12+x=5x-20\)
\(-12+20=5x-x=4x\)
\(\Rightarrow8=4x\)
\(\Leftrightarrow x=2\)
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\(3^{x+4}=9^{2x-1}\)
\(\Rightarrow3^{x+4}=3^{4x-2}\)
\(\Rightarrow x+4=4x-2\)
\(\Rightarrow3x=6\Rightarrow x=2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2x^4-x^3+2x^2+1=2x^4-2x^3+2x^2+x^3-x^2+x+x^2-x+1\\ \)
\(=2x^2\left(x^2-x+1\right)+x\left(x^2-x+1\right)+\left(x^2-x+1\right)=\left(x^2-x+1\right)\left(2x^2+x+1\right)\)
Vậy a = 2; b = 1; c = 1.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(|2x+3|=x+2\)
=> 2x+3=x+2 hoặc -(2x+3)=x+2
=>2x-x=2-3 -2x-3=x+2
=> x=-1 -2-3=x+2x
-5=3x => x=-5/3
Vậy x=-1; -5/3.Em tham khảo rồi cho chị biết đúng hay sai nha!
\(\left|2x+3\right|=x+2\)
\(\Leftrightarrow\orbr{\begin{cases}2x+3=x+2\\2x+3=-x-2\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}2x-x=2-3\\2x+x=-2-3\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-1\\3x=-5\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-1\\x=-\frac{5}{3}\end{cases}}\)
Vậy \(x\in\left\{-\frac{5}{3};-1\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x+2x+3x+...+100x=2200\)
=>\(x\left(1+2+3+...+100\right)=2200\)
=>\(x.\frac{100.101}{2}=2200\)
=>\(x.5050=2200\)
=>x=2200:5050
=>x=\(\frac{44}{101}\)
\(x+2x+3x+...+100x=220\)
\(\Rightarrow x\left(1+2+3+....+100\right)=2200\)
\(\Rightarrow5050x=2200\)
\(\Rightarrow x=\frac{44}{101}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{2x-1}{3}=\dfrac{2-x}{-2}\)
\(\Rightarrow-2\left(2x-1\right)=3\left(2-x\right)\)
\(\Rightarrow-4x+2=6-3x\Rightarrow x=-4\)
Giải:
\(2^{2x}.4^x=256\)
\(\Leftrightarrow\left(2^2\right)^x.4^x=256\)
\(\Leftrightarrow4^x.4^x=256\)
\(\Leftrightarrow\left(4.4\right)^x=256\)
\(\Leftrightarrow16^x=256\)
\(\Leftrightarrow16^x=16^2\)
Vì 16 = 16
Nên x = 2
Vậy x = 2.
Chúc bạn học tốt!!!
22x.(22)x=28
2(2x+2x)=2 mũ 8
24x=28
\(\Rightarrow\)4x=8
x=2
vậu x=2