\(x^2-10x+25=0\)
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a) \(7x\left(x+1\right)-3\left(x+1\right)=0\Rightarrow\left(x+1\right)\left(7x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+1=0\\7x+3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x=-\dfrac{3}{7}\end{matrix}\right.\)
b) 3(x + 8) - x2 - 8x = 0
=> 3(x + 8) - (x2 + 8x) = 0
=> 3(x + 8) - x(x + 8) = 0
=> (x + 8)(3 - x) = 0 => \(\left[{}\begin{matrix}x+8=0\\3-x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-8\\x=3\end{matrix}\right.\)
c) \(x^2-10x=-25\Rightarrow x^2-10x+25=0\Rightarrow\left(x-5\right)^2=0\Rightarrow x=5\)
d) Giống câu c
a)
b) 3(x + 8) - x2 - 8x = 0
=> 3(x + 8) - (x2 + 8x) = 0
=> 3(x + 8) - x(x + 8) = 0
=> (x + 8)(3 - x) = 0 =>
c)
![](https://rs.olm.vn/images/avt/0.png?1311)
`a, x^2-10x+25=0`
`<=>x^2 -2.x.5+5^2=0`
`<=>(x-5)^2=0`
`<=>x-5=0`
`<=>x=5`
__
`x^2 -8x+16=0`
`<=> x^2 - 2.x.4+4^2=0`
`<=>(x-4)^2=0`
`<=>x-4=0`
`<=>x=4`
__
`x^2-49=0`
`<=>x^2 - 7^2=0`
`<=>(x-7)(x+7)=0`
`<=>x-7=0` hoặc `x+7=0`
`<=> x=7` hoặc `x=-7`
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`4x^2-25=0`
`<=> (2x)^2 -5^2=0`
`<=>(2x-5)(2x+5)=0`
`<=>2x-5=0` hoặc `2x+5=0`
`<=> 2x=5` hoặc `2x=-5`
`<=>x=5/2` hoặc `x=-5/2`
a: =>(x-5)^2=0
=>x-5=0
=>x=5
b: =>(x-4)^2=0
=>x-4=0
=>x=4
c: =>(x-7)(x+7)=0
=>x-7=0 hoặc x+7=0
=>x=7 hoặc x=-7
d: =>(2x-5)(2x+5)=0
=>2x-5=0 hoặc 2x+5=0
=>x=5/2 hoặc x=-5/2
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\sqrt{x^2-25}+\sqrt{x^2+10x+25}=0.\)
\(\Rightarrow\sqrt{x^2-5^2}+\sqrt{x^2+2.5.x+5^2}=0\)
\(\Rightarrow\sqrt{\left(x-5\right).\left(x+5\right)}+\sqrt{\left(x+5\right)^2}=0\)
\(\Rightarrow\sqrt{\left(x+5\right).\left(x-5+1\right)}=0\)
\(\Rightarrow\hept{\begin{cases}x+5=0\\x-5+1=0\end{cases}}\Rightarrow\hept{\begin{cases}x=-5\\x-4=0\end{cases}}\Rightarrow\hept{\begin{cases}x=-5\\x=4\end{cases}}\)
Vậy \(x=\hept{\begin{cases}-5\\4\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^2-5x-4\left(x-5\right)=0\)
\(\Leftrightarrow\)\(x\left(x-5\right)-4\left(x-5\right)=0\)
\(\Leftrightarrow\)\(\left(x-5\right)\left(x-4\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x-5=0\\x-4=0\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=5\\x=4\end{cases}}\)
Vậy....
\(2x\left(x+6\right)=7x+42\)
\(\Leftrightarrow\)\(2x\left(x+6\right)-7x-42=0\)
\(\Leftrightarrow\)\(2x\left(x+6\right)-7\left(x+6\right)=0\)
\(\Leftrightarrow\)\(\left(x+6\right)\left(2x-7\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x+6=0\\2x-7=0\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=-6\\x=\frac{7}{2}\end{cases}}\)
Vậy......
\(x^3-5x^2+x-5=0\)
\(\Leftrightarrow\)\(x^2\left(x-5\right)+\left(x-5\right)=0\)
\(\Leftrightarrow\)\(\left(x-5\right)\left(x^2+1\right)=0\)
\(\Leftrightarrow\)\(x-5=0\)
\(\Leftrightarrow\)\(x=5\)
\(x^4-2x^3+10x^2-20x=0\)
\(\Leftrightarrow\)\(x^3\left(x-2\right)+10x\left(x-2\right)=0\)
\(\Leftrightarrow\)\(x\left(x-2\right)\left(x^2+10\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\\x-2=0\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\\x=2\end{cases}}\)
Vậy...
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow x^2-10x+25-4x^2-20x=0\)
\(\Leftrightarrow-3x^2-30x+25=0\)
\(\Leftrightarrow3x^2+30x-25=0\)
\(\text{Δ}=30^2-4\cdot3\cdot\left(-25\right)=900+300=1200>0\)
Do đó: Phương trình có hai nghiệm phân biệt là:
\(\left\{{}\begin{matrix}x_1=\dfrac{-30-20\sqrt{3}}{6}=\dfrac{-15-10\sqrt{3}}{3}\\x_2=\dfrac{-15+10\sqrt{3}}{3}\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow\left(x-5\right)^2=0\\ \Leftrightarrow x-5=0\\ \Leftrightarrow x=5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(2x-3\right)^2-x^2+10x-25=0\)
\(\left(2x-3\right)^2-\left(x-5\right)^2=0\)
\(\left(2x-3+x-5\right)\left(2x-3-x+5\right)=0\)
\(\left(3x-8\right)\left(x+2\right)=0\)
\(\Rightarrow3x-8=0\)hoặc \(x+2=0\)
=> \(x=\frac{8}{3}\) hoặc \(x=-2\)
\(x^2-10x+25=0\)
\(\left(x-5\right)^2=0\) ( sử dụng hằng đẳng thức bình phương của 1 hiệu)
\(\Rightarrow x-5=0\)
\(\Rightarrow x=5\)
vậy \(x=5\)
\(x^2-10x+25=0\)
\(x^2-2.5x+5^2=0\)
\(\left(x-5\right)^2=0\)
\(\Rightarrow x-5=0\)
\(\Rightarrow x=5\)