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23 tháng 10 2016
a) \(4x^2-12x=-9\)
\(\Leftrightarrow4x^2-12x+9=0\)
\(\Leftrightarrow\left(2x-3\right)^2=0\)
\(\Leftrightarrow2x-3=0\Leftrightarrow x=\frac{3}{2}\)
b) \(\left(5-2x\right)\left(2x+7\right)=4x^2-25\)
\(\Leftrightarrow\left(5-2x\right)\left(2x+7\right)+\left(25-4x^2\right)=0\)
\(\Leftrightarrow\left(5-2x\right)\left(2x+7\right)+\left(5-2x\right)\left(5+2x\right)=0\)
\(\Leftrightarrow\left(5-2x\right)\left(2x+7+5+2x\right)=0\)
\(\Leftrightarrow\left(5-2x\right)\left(4x+12\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\frac{5}{2}\\x=-3\end{array}\right.\)
c)\(x^3+27+\left(x+3\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9+x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-2x\right)=0\)
\(\Leftrightarrow\left(x+3\right)x\left(x-2\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=-3\\x=0\\x=2\end{array}\right.\)
d) \(4\left(2x+7\right)^2-9\left(x+3\right)^2=0\)
\(\Leftrightarrow\left[2\left(2x+7\right)-3\left(x+3\right)\right]\left[2\left(2x+7\right)+3\left(x+3\right)\right]=0\)
\(\Leftrightarrow\left(4x+14-3x-9\right)\left(4x+14+3x+9\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(7x+23\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=-5\\x=-\frac{23}{17}\end{array}\right.\)
28 tháng 9 2019
a)\(\left(x-1\right)^3+3\left(x+1\right)^2=\left(x^2-2x+4\right)\left(x+2\right)\)
\(\Leftrightarrow x^3-3x^2+3x-1+3\left(x^2+2x+1\right)=x^3+8\)
\(\Leftrightarrow-3x^2+3x+3x^2+6x+3=9\)
\(\Leftrightarrow9x=6\Leftrightarrow x=\frac{2}{3}\)
b) \(x^2-4=8\left(x-2\right)\)
\(\Leftrightarrow x^2-4=8x-16\)
\(\Leftrightarrow x^2-8x+12=0\)
\(\Leftrightarrow x^2-2x-6x+12=0\)
\(\Leftrightarrow x\left(x-2\right)-6\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-6\right)\left(x-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-6=0\\x-2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=6\\x=2\end{cases}}\)
28 tháng 9 2019
c) \(x^2-4x+4=9\left(x-2\right)\)
\(\Leftrightarrow\left(x-2\right)^2=9\left(x-2\right)\)
\(\Leftrightarrow\left(x-2\right)^2-9\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-11\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\x-11=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2\\x=11\end{cases}}\)
d) \(4x^2-12x+9=\left(5-x\right)^2\)
\(\Leftrightarrow\left(2x-3\right)^2=\left(5-x\right)^2\)
\(\Leftrightarrow\orbr{\begin{cases}2x-3=5-x\\2x-3=x-5\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{8}{3}\\x=-2\end{cases}}\)
21 tháng 7 2017
1) \(\left(x+1\right)^3-\left(x-1\right)^3=6.\left(x+2\right)^2-9\)
\(\Leftrightarrow x^3+3x^2+3x+1-\left(x^3-3x^2+3x-1\right)=6\left(x^2+4x+4\right)-9\)
\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1=6x^2+24x+24-9\)
\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1-6x^2-24x-24+9=0\)
\(\Leftrightarrow-24x-13=0\Leftrightarrow-24x=13\Leftrightarrow x=\dfrac{-13}{24}\) vậy \(x=\dfrac{-13}{24}\)
21 tháng 7 2017
2) \(\left(2x-1\right).\left(4x^2+2x+1\right)+\left(1-2x\right)^3=3.\left(2x+3\right)^2\)
\(\Leftrightarrow8x^3+4x^2+2x-4x^2-2x-1+1-6x+12x^2-8x^3=3\left(.4x^2+12x+9\right)\)
\(\Leftrightarrow8x^3+4x^2+2x-4x^2-2x-1+1-6x+12x^2-8x^3=12x^2+36x+27\)
\(\Leftrightarrow8x^3+4x^2+2x-4x^2-2x-1+1-6x+12x^2-8x^3-12x^2-36x-27=0\)
\(\Leftrightarrow-42x-27=0\Leftrightarrow-42x=27\Leftrightarrow x=\dfrac{-27}{42}\) vậy \(x=\dfrac{-27}{42}\)
4 tháng 7 2018
a) \(\left(x+3\right)^2-\left(2x+1\right).\left(2x-1\right)=22\)
\(\Leftrightarrow x^2+6x+9-\left(4x^2-1\right)=22\)
\(\Leftrightarrow x^2+6x+9-4x^2+1=22\)
\(\Leftrightarrow-3x^2+6x-12=0\)
\(\Leftrightarrow x^2-2x+4=0\)
\(\Leftrightarrow\left(x^2-2x+1\right)+3=0\)
\(\Leftrightarrow\left(x-1\right)^2+3=0\)(vô lý)
b) \(\left(4x+3\right)\left(4x-3\right)-\left(4x-5\right)^2=46\)
\(\Leftrightarrow16x^2-9-\left(16x^2-40x+25\right)=46\)
\(\Leftrightarrow16x^2-9-16x^2+40x-25-46=0\)
\(\Leftrightarrow40x-80=0\)
\(\Leftrightarrow x=2\)
AM
14 tháng 7 2018
\(b,\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2+2\right)=15\)
\(\Leftrightarrow x^3+8-x^3-2x=15\)
\(\Leftrightarrow-2x=15-8=7\)
\(\Leftrightarrow x=\frac{-7}{2}\)
Vậy \(x=\frac{-7}{2}\)
7 tháng 8 2017
a)Dat \(x^2-4x+3=a;x^2-7x+6=b \Rightarrow a+b=2x^2-11x+9\)
....
(2x+1)22−4x.(x+3)=9
(2x+1)(2x+1)
−4x.(x+3)=9
2x(2x+1) + 1(2x+1) - 4x.(x+3)=9
4x2 + 2x + 2x + 1 - 4x.(x+3)=9
4x2+4x+1-4x.(x+3)=9
4x2+4x+1-4x2- 12x =9
4x2+4x+1-4x2 - 12x =9
4x2 - 4x2 +4x+1- 12x =9
4x+1- 12x =9
4x-12x+1 =9
-8x+1 =9
-8x=9-1
-8x=8
x=8: -8
x= -1