Tìm x, biết: 4x^2-4x-3=0
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4 tháng 8 2016
a)\(x^2+10x=24\)
\(\Leftrightarrow x^2+10x-24=0\)
\(\Leftrightarrow x^2-2x+12x-24=0\)
\(\Leftrightarrow x\left(x-2\right)+12\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+12\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x-2=0\\x+12=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=2\\x=-12\end{array}\right.\)
b)\(4x^2+4x=24\)
\(\Leftrightarrow4x^2+4x-24=0\)
\(\Leftrightarrow4\left(x^2+x-6\right)=0\)
\(\Leftrightarrow x^2+x-6=0\)
\(\Leftrightarrow x^2+3x-2x-6=0\)
\(\Leftrightarrow x\left(x+3\right)-2\left(x+3\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x-2=0\\x+3=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=2\\x=-3\end{array}\right.\)
c)\(4x^2-4x=48\)
\(\Leftrightarrow4x^2-4x-48=0\)
\(\Leftrightarrow4\left(x^2-x-12\right)=0\)
\(\Leftrightarrow x^2-x-12=0\)
\(\Leftrightarrow x^2+3x-4x-12=0\)
\(\Leftrightarrow x\left(x+3\right)-4\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x+3=0\\x-4=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=-3\\x=4\end{array}\right.\)
4 tháng 8 2016
\(a,x^2+10x=24\)
\(\Leftrightarrow x^2+10x-24=0\)
\(\Leftrightarrow x^2-2x+12x-24=0\)
\(\Leftrightarrow x\left(x-2\right)+12\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+12\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x-2=0\\x+12=0\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=2\\x=-12\end{array}\right.\)
\(\text{Vậy x=2 hoặc x=-12 }\)
\(b,4x^2+4x=24\)
\(\Leftrightarrow4x^2+4x-24=0\)
\(\Leftrightarrow4x^2-8x+12x-24=0\)
\(=4x\left(x-2\right)+12\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(4x+12\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x-2=0\\4x+12=0\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=2\\x=-3\end{array}\right.\)
Vậy hoặc \(\text{Vậy x=2 hoặc x=-3 }\)
\(c,4x^2-4x=48\)
\(\Leftrightarrow4x^2-4x-48=0\)
\(\Leftrightarrow\left[\left(2x\right)^2-2.2x+1^2\right]-1^2-48=0\)
\(\Leftrightarrow\left(2x-1\right)^2-49=0\)
\(\Leftrightarrow\left(2x-1\right)^2-7^2=0\)
\(\Leftrightarrow\left(2x-1-7\right)\left(2x-1+7\right)=0\)
\(\Leftrightarrow\left(2x-8\right)\left(2x+6\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}2x-8=0\\2x+6=0\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=4\\x=-3\end{array}\right.\)
\(\text{Vậy x=4 hoặc x=-3
}\)
NB
1
9 tháng 5 2017
ta có x-y+2xy=3<=>2x-2y+4xy=6<=>2x(2y+1)-(2y+1)=5<=>(2x-1)(2y+1)=7
Vì (2x-1)(2y+1)=7 => \(2x-1\inƯ\left(7\right)\)={1,-1,7,-7}{}
=>\(x\in\){1,0,4,-3}=> y\(\in\){3,-4,0,-1}
10 tháng 5 2017
Ta có:
x - y + 2xy = 3
Suy ra 2x - 2y + 4xy = 6
Suy ra 2x( 2y + 1 ) - ( 2y + 1 ) = 5
Suy ra ( 2x - 1 ) ( 2y + 1 ) = 7
Vì ( 2x - 1 ) ( 2y + 1 ) = 7
Suy ra 2x -1 thuộc Ư (7) = { 1 ; -1 ; 7 ; -7 }
Suy ra x thuộc { 1 ; 0 ; 4 ; -3 }
y thuộc { 3 ; -4 ; 0 ; -1 }
HY
0
Bài làm:
Ta có: \(4x^2-4x-3=0\)
\(\Leftrightarrow\left(4x^2-4x+1\right)-4=0\)
\(\Leftrightarrow\left(2x-1\right)^2-2^2=0\)
\(\Leftrightarrow\left(2x-3\right)\left(2x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x-3=0\\2x+1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{3}{2}\\x=-\frac{1}{2}\end{cases}}\)
Ta có : \(4x^2-4x-3=0\)
\(\Leftrightarrow\left(4x^2-4x+1\right)-4=0\)
\(\Leftrightarrow\left(2x-1\right)^2=4\)
\(\Leftrightarrow\orbr{\begin{cases}2x-1=2\\2x-1=-2\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{3}{2}\\x=-\frac{1}{2}\end{cases}}\)
Vậy \(x\in\left\{\frac{3}{2};-\frac{1}{2}\right\}\)