x^2+x-12=0 tìm x
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1) -12+3.(-x+7)=-18
3.(-x+7)=-18+12
3.(x+7)=-6
x+7=-6:3
x+7=-2
x=-2-7
x=-9
1: Để A>0 thì x-1<0
hay x<1
Kết hợp ĐKXĐ, ta được: \(0\le x< 1\)
1) Để A > 0 thì:
\(x-1< 0\Leftrightarrow x< 1\)
\(\Rightarrow0\le x< 1\) và \(x\ne1\)
2) \(A=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}=1+\dfrac{2}{\sqrt{x}-1}\)
Để A<1 thì \(\dfrac{2}{\sqrt{x}-1}< 0\)
\(\Rightarrow\sqrt{x}-1< 0\Leftrightarrow\sqrt{x}< 1\)
Mà x\(\ge0,x\ne1\)
\(\Rightarrow0\le x< 1\)
Lời giải:
$x^2+x-12=0$
$\Leftrightarrow (x^2-3x)+(4x-12)=0$
$\Leftrightarrow x(x-3)+4(x-3)=0$
$\Leftrightarrow (x-3)(x+4)=0$
$\Leftrightarrow x-3=0$ hoặc $x+4=0$
$\Leftrightarrow x=3$ hoặc $x=-4$
a) \(x^3\)\(-\)\(\frac{1}{4}x\)\(=\)\(0\)
\(x\left(x^2-\frac{1}{4}\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\\x^2-\frac{1}{4}=0\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\\x^2=0,5^2\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\\x=+-0,5\end{cases}}\)
Vậy .............................
b) \(\left(2x-1\right)^2\)\(-\)\(\left(x+3\right)^2\)\(=\)\(0\)
\(\left(2x-1+x+3\right)\left(2x-1-x-3\right)=0\)
\(\left(3x+2\right)\left(x-4\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}3x+2=0\\x-4=0\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}3x=-2\\x=4\end{cases}}\)\(\orbr{\begin{cases}x=\frac{-2}{3}\\x=4\end{cases}}\)
Vậy ................................
c) \(x^2\)\(\left(x-3\right)\)\(+\)\(12\)\(-\)\(4x\)\(=\)\(0\)
\(x^2\)\(\left(x-3\right)\)\(-\)\(4\)\(\left(x-3\right)\)\(=\)\(0\)
\(\left(x^2-4\right)\left(x-3\right)\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x^2\\x-3=0\end{cases}-4=0}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x^2\\x=3\end{cases}=2^2}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x=+-2\\x=3\end{cases}}\)
a)\(x^3-\frac{1}{4}x=0\)
\(\Leftrightarrow x\left(x^2-\frac{1}{4}\right)=0\)
\(\Leftrightarrow x\left(x-\frac{1}{2}\right)\left(x+\frac{1}{2}\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}x=0\\x-\frac{1}{2}=0\\x+\frac{1}{2}=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=0\\x=\frac{1}{2}\\x=-\frac{1}{2}\end{cases}}}\)
\(\left(x+12\right)\left(x-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+12=0\\x-3=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-12\\x=3\end{cases}}\)
\(x\left(x+2\right)\left(7-x\right)=0\)
\(\Rightarrow x=0\) hoặc \(\orbr{\begin{cases}x+2=0\\7-x=0\end{cases}}\)
\(\Rightarrow x=0\) hoặc \(\orbr{\begin{cases}x=-2\\x=7\end{cases}}\)
( x - 12 ).( x - 5 ) = 0
x . ( 12 - 5 ) = 0
x. 7 = 0
x = 0 : 7
x = 0
( x - 2 ).(x + 3 ) = 0
x. ( 2 + 3 ) = 0
x . 5 = 0
x = 0 : 5
x = 0
kb vs mk nha
chúc bạn học tốt nhé !
\(\left(x-12\right).\left(x-5\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-12=0\\x-5=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=12\\x=5\end{cases}}\)
\(\left(x-2\right).\left(x+3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-2=0\\x+3=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2\\x=-3\end{cases}}\)
\(x^3-8-\left(x-2\right)\left(x-12\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^2+2x+4-x+12\right)=0\)
\(\Leftrightarrow x-2=0\)
hay x=2
\(\Leftrightarrow\left(x-2\right)\left(x^2+2x+4\right)-\left(x-2\right)\left(x-12\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x^2+2x+4-x+12\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x^2+x+16\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\\left(x+\dfrac{1}{2}\right)^2+\dfrac{63}{4}=0\left(vô.lí\right)\end{matrix}\right.\\ \Leftrightarrow x=2\)