Giúp mình với
x2-x-2=0
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a) (x-3)3-3+x=0
=> (x-3)3+(x-3)=0
=> (x-3)(x2-6x+10)
=> \(\left[{}\begin{matrix}x-3=0\\x^2-6x+10=0\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=3\\\left(x-3\right)^2=1\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=3\\x=4\\x=2\end{matrix}\right.\)
x(x + 3) = 0
=> \(\orbr{\begin{cases}x=0\\x+3=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=0\\x=0-3\end{cases}}\)
=> \(\orbr{\begin{cases}x=0\\x=-3\end{cases}}\)
(x - 2) (5 - x) = 0
=> \(\orbr{\begin{cases}x-2=0\\5-x=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=0+2\\x=5-0\end{cases}}\)
=> \(\orbr{\begin{cases}x=2\\x=5\end{cases}}\)
(x - 1) (x2 + 1) = 0
=> \(\orbr{\begin{cases}x-1=0\\x^2+1=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=0+1\\x^2=0-1\end{cases}}\)
=> \(\orbr{\begin{cases}x=1\\x^2=-1\end{cases}}\)
=> \(\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)
x(x+3) = 0
→ x = 0
hoặc x + 3 = 0
⇒ x = 0
hoặc x = -3
Vậy x ∈ { 0 ; -3 }
( x -2 ) ( 5 -x ) = 0
⇒ x - 2 = 0
hoặc 5 - x = 0
⇒ x = 2
hoặc x= 5
Vậy x∈ { 2 ; 5 }
\(\left(x-\dfrac{3}{2}\right)\times\left(2x+1\right)>0\)
Th1:
\(x-\dfrac{3}{2}>0\Leftrightarrow x>\dfrac{3}{2}\)
\(2x+1>0\Leftrightarrow2x>1\Leftrightarrow x>\dfrac{1}{2}\)
( 1 )
Th2:
\(x-\dfrac{3}{2}< 0\Leftrightarrow x< \dfrac{3}{2}\)
\(2x+1< 0\Leftrightarrow2x< -1\Leftrightarrow x< -\dfrac{1}{2}\)
( 2 )
Từ ( 1 ) và ( 2 ), ta có:
\(\Rightarrow x< -\dfrac{1}{2};x>\dfrac{3}{2}\)
\(\left(2-x\right)\times\left(\dfrac{4}{5}-x\right)< 0\)
Th1:
\(2-x>0\Leftrightarrow x>2\)
\(\dfrac{4}{5}-x< 0\Leftrightarrow x< \dfrac{4}{5}\)
( Loại )
Th2:
\(2-x< 0\Leftrightarrow x< 2\)
\(\dfrac{4}{5}-x>0\Leftrightarrow x>\dfrac{4}{5}\)
=> \(\dfrac{4}{5}< x< 2\)
\(\Leftrightarrow\left(x-2\right)\left(x^2+2x+4\right)-\left(x-2\right)\left(x-12\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x^2+x+16\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-2=0\\\left(x+\dfrac{1}{2}\right)^2+\dfrac{63}{4}=0\left(vô.lí\right)\end{matrix}\right.\\ \Leftrightarrow x=2\)
x^2+12x-13=0
= x2 + 13x - x - 13 = 0
= x ( x + 13 ) - ( x + 13 ) = 0
= ( x - 1 ) ( x + 13 )
= 0
= x = 1
= x = -13
Hok tốt
x2+12x=13
xx+12x=13
x.(12+x)=13
x=0
hoặc x+12=0=> x= -12
Vậy, x = 0 hoặc x =-12
\(\left(x-2\right)\left(4x-20\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\4x-20=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\4x=20\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\\ \left(x-5\right)\left(25-5x?\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-5=0\\25-5x=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\5x=25\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\x=5\end{matrix}\right.\\ \left(x-4\right)\left(2x-8\right)\\ \Rightarrow\left[{}\begin{matrix}x-4=0\\2x-8=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\2x=8\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\x=4\end{matrix}\right.\)
a,(x-2)(4x-20)=0
=>x-2=0 hoặc 4x-20=0
=>x=2 hoặc x=5
b,(x-5)(25-5)=0
=>x-5=0 ( vì 25-5 ≠0)
=>x=5
c,(x-4)(2x-8)=0
=>x-4=0 hoặc 2x-8=0
=>x=4
x^2-x-2=0
x^2-2x+x-2=0
x(x-2)+(x-2)=0
(x+1)(x-2)=0
\(\Rightarrow\hept{\begin{cases}x+1=0\\x-2=0\end{cases}\Rightarrow\hept{\begin{cases}x=-1\\x=2\end{cases}}}\)