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Câu 11:
Ta có: \(\left(2x-3\right)\left(3x+2\right)-\left(2x-3\right)^2=-18\)
\(\Leftrightarrow6x^2+4x-9x-6-4x^2+12x-9=-18\)
\(\Leftrightarrow2x^2+7x+3=0\)
\(\Leftrightarrow\left(x+3\right)\left(2x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-\dfrac{1}{2}\end{matrix}\right.\)
b: Xét ΔABD và ΔBAC có
BA chung
BD=AC
AD=BC
Do đó: ΔABD=ΔBAC
c: ta có: EA+EC=AC
EB+ED=BD
mà AC=BD
và EA=EB
nên EC=ED
Câu I:
1: Ta có: 4x-3=2x+7
nên 2x=10
hay x=5
2: Ta có: \(\left|x-2\right|=4-2x\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=4-2x\left(x\ge2\right)\\x-2=2x-4\left(x< 2\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=6\\-x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\left(nhận\right)\\x=2\left(loại\right)\end{matrix}\right.\)
3: ta có: \(\left(x-1\right)\left(x-2\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=-1\end{matrix}\right.\)
11)11) 3x(x-5)2-(x+2)3+2(x-1)3-(2x+1)(4x2-2x+1)=3x(x2-10x+25)-(x3+6x2+12x+8)+2(x3-3x2+3x-1)-(8x3+1)=3x3-30x2+75x-x3-6x2-12x-8+2x3-6x2+6x-2-8x3-1=-4x3-42x2+63x-11
\(\left(x-5\right)\left(x+5\right)-\left(x+3\right)^2+3\left(x-2\right)^2=\left(x+1\right)^2-\left(x-4\right)\left(x+4\right)+3x^2\)\(\Leftrightarrow x^2-25-\left(x^2+6x+9\right)+3\left(x^2-4x+4\right)=x^2+2x+1-\left(x^2-4^2\right)+3x^2\)\(\Leftrightarrow x^2-25-x^2-6x-9+3x^2-12x+12=x^2+2x+1-x^2+16+3x^2\)
\(\Leftrightarrow-20x=39\)
\(\Leftrightarrow x=\frac{-39}{20}\)
Vậy \(x=\frac{-39}{20}\)
a: Ta có: \(25x^2\left(x-y\right)-x+y\)
\(=\left(x-y\right)\left(25x^2-1\right)\)
\(=\left(x-y\right)\left(5x-1\right)\left(5x+1\right)\)
b: Ta có: \(16x^2\left(z^2-y^2\right)-z^2+y^2\)
\(=\left(z^2-y^2\right)\left(16x^2-1\right)\)
\(=\left(z-y\right)\left(z+y\right)\left(4x-1\right)\left(4x+1\right)\)
c: Ta có: \(x^3+x^2y-x^2z-xyz\)
\(=x^2\left(x+y\right)-xz\left(x+y\right)\)
\(=x\left(x+y\right)\left(x-z\right)\)