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Câu 2 sai đề nhé
Phải là:(x-999)/99+(x-896)/101+(x-789/103)=6
Mấy bài dài dài kia tí mình làm cho :)
( x - 1 )3 - x( x - 2 )2 + 1
= x3 - 3x2 + 3x - 1 - x( x2 - 4x + 4 ) + 1
= x3 - 3x2 + 3x - x3 + 4x2 - 4x
= x2 - x = x( x - 1 )
2x( 3x + 2 ) - 3x( 2x + 3 )
= 6x2 + 4x - 6x2 - 9x
= -5x
( x + 2 )3 + ( x - 3 )2 - x2( x + 5 )
= x3 + 6x2 + 12x + 8 + x2 - 6x + 9 - x3 - 5x2
= 2x2 + 6x + 17
( 2x + 3 )( x - 5 ) + 2x( 3 - x ) + x - 10
= 2x2 - 7x - 15 + 6x - 2x2 + x - 10
= -25
( x + 5 )( x2 - 5x + 25 ) - x( x - 4 )2 + 16x
= x3 + 53 - x( x2 - 8x + 16 ) + 16x
= x3 + 125 - x3 + 8x2 - 16x + 16
= 8x2 + 125
( -x - 2 )3 + ( 2x - 4 )( x2 + 2x + 4 ) - x2( x - 6 )
= -x3 - 6x2 - 12x - 8 + 2x3 - 16 - x3 + 6x2
= -12x - 24 = -12( x + 2 )
Tương tự ...
a, \(\left(x-1\right)^3-x\left(x-2\right)^2+1=x^3-3x^2+3x-1-x^3+4x^2-4x+1=x^2-x\)
b, \(2x\left(3x+2\right)-3x\left(2x+3\right)=6x^2+4x-6x^2-9x=-5x\)
c, \(\left(x+2\right)^3+\left(x-3\right)^2-x^2\left(x+5\right)=x^3+6x^2+12x+8+x^2+6x+9-x^3-5x^2=2x^2+18x+17\)
a) \(2x\left(x-3\right)+5\left(x-3\right)=0\)
\(\Rightarrow\left(x-3\right)\left(2x+5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\2x+5=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\2x=-5\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{5}{2}\end{matrix}\right.\)
b) \(\left(x^2-4\right)-\left(x-2\right)\left(3-2x\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x+2\right)-\left(x-2\right)\left(3-2x\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x+2-3+2x\right)=0\)
\(\Rightarrow\left(x-2\right)\left(3x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\3x-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\3x=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{1}{3}\end{matrix}\right.\)
c) \(\left(2x+5\right)^2=\left(x+2\right)^2\)
\(\Rightarrow\left(2x+5\right)^2-\left(x+2\right)^2=0\)
\(\Rightarrow\left(2x+5-x-2\right)\left(2x+5+x+2\right)=0\)
\(\Rightarrow\left(x+3\right)\left(3x+7\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+3=0\\3x+7=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-3\\3x=-7\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-3\\x=-\dfrac{7}{3}\end{matrix}\right.\)
d) \(x^2-5x+6=0\)
\(\Rightarrow x^2-2x-3x+6=0\)
\(\Rightarrow x\left(x-2\right)-3\left(x-2\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x-3=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
e) \(2x^3+6x^2=x^2+3x\)
\(\Rightarrow2x^3+6x^2-x^2-3x=0\)
\(\Rightarrow2x^3+5x^2-3x=0\)
\(\Rightarrow x\left(2x^2+5x-3\right)=0\)
\(\Rightarrow2x^2+5x-3=0\)
\(\Rightarrow2x^2-6x+x-3=0\)
\(\Rightarrow2x\left(x-3\right)+\left(x-3\right)=0\)
\(\Rightarrow\left(x-3\right)\left(2x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\2x+1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{1}{2}\end{matrix}\right.\)
f) \(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)-2x^2\)
\(\Rightarrow\left(x^2-1\right)\left(x+2\right)-\left(x^3-8\right)-2x^2=0\)
\(\Rightarrow x^3+2x^2-x+2-x^3+8-2x^2=0\)
\(\Rightarrow-x+10=0\)
\(\Rightarrow x=10\)
\(a,x^4-16x^2+32x-16=0\)
\(\Leftrightarrow\left(x^4-16\right)-16x\left(x-2\right)=0\)
\(\Leftrightarrow\left(x^4+4\right)\left(x-2\right)\left(x+2\right)-16x\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^3+2x^2-12x+8\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^3-2x^2+4x^2-8x-4x+8\right)=0\)\(\Leftrightarrow\left(x-2\right)\left[x^2\left(x-2\right)+4x\left(x-2\right)-4\left(x-2\right)\right]=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-2\right)\left(x^2+4x-4\right)=0\)
\(\Leftrightarrow\left(x-2\right)^2\left[\left(x+2\right)^2-8\right]=0\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^2=0\\\left(x+2\right)^2-8=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-2=0\\\left(x+2\right)^2=8\Rightarrow\left[{}\begin{matrix}x+2=\sqrt{8}\\x+2=-\sqrt{8}\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\sqrt{8}-2\\x=-\sqrt{8}-2\end{matrix}\right.\)
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tham khảo nhé !!! chúc bạn học tốt
a. 5-(x-6)=4(3-2x)
<=>5-x+6 = 12-8x
<=>-x+8x =-5-6+12
<=>7x=1
<=>x=\(\frac{1}{7}\)
Vậy phương trình có nghiệm là S= ( \(\frac{1}{7}\))
c.7 -(2x+4) =-(x+4)
<=> 7-2x-4=-x-4
<=>-2x+x= -7+4-4
<=> -x = -7
<=> x=7
Vậy phương trình có nghiệm là S=(7)