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18, \(\frac{x}{2}+\frac{x^2}{8}=0\Leftrightarrow4x+x^2=0\Leftrightarrow x\left(x+4\right)=0\Leftrightarrow x=-4;x=0\)
19, \(4-x=2\left(x-4\right)^2\Leftrightarrow\left(4-x\right)-2\left(4-x\right)^2=0\)
\(\Leftrightarrow\left(4-x\right)\left[1-2\left(4-x\right)\right]=0\Leftrightarrow\left(4-x\right)\left(-7+2x\right)=0\Leftrightarrow x=4;x=\frac{7}{2}\)
20, \(\left(x^2+1\right)\left(x-2\right)+2x-4=0\Leftrightarrow\left(x^2+1\right)\left(x-2\right)+2\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^2+3>0\right)=0\Leftrightarrow x=2\)
21, \(x^4-16x^2=0\Leftrightarrow x^2\left(x-4\right)\left(x+4\right)=0\Leftrightarrow x=0;x=\pm4\)
22, \(\left(x-5\right)^3-x+5=0\Leftrightarrow\left(x-5\right)^3-\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left[\left(x-5\right)^2-1\right]=0\Leftrightarrow\left(x-5\right)\left(x-6\right)\left(x-4\right)=0\Leftrightarrow x=4;x=5;x=6\)
23, \(5\left(x-2\right)-x^2+4=0\Leftrightarrow5\left(x-2\right)-\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(5-x-2\right)=0\Leftrightarrow x=2;x=3\)
Xét tứ giác ABEC có
AB//EC
AC//BE
Do đó: ABEC là hình bình hành
Suy ra: AC=BE
mà AC=BD
nên BE=BD
hay ΔBED cân tại B





Mọi Người giải giúp em ạ em cảm ơn ạ 

giúp mik gấp vs mng. Làm hết hộ mik ạ. Mik cảm ơn







a: 2x+3=x+1
=>2x-x=1-3
=>x=-2
b: \(2x\left(2x-1\right)-\left(2x+3\right)^2=5\)
=>\(4x^2-2x-4x^2-12x-9=5\)
=>-14x=9+5=14
=>x=-1
c: \(4x^2-25\left(x+2\right)^2=0\)
=>\(\left(2x\right)^2-\left(5x+10\right)^2=0\)
=>(2x-5x-10)(2x+5x+10)=0
=>(-3x-10)(7x+10)=0
=>(3x+10)(7x+10)=0
=>\(\left[\begin{array}{l}3x+10=0\\ 7x+10=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-\frac{10}{3}\\ x=-\frac{10}{7}\end{array}\right.\)
d: \(2x^2+7x+5=0\)
=>\(2x^2+2x+5x+5=0\)
=>2x(x+1)+5(x+1)=0
=>(x+1)(2x+5)=0
=>\(\left[\begin{array}{l}x+1=0\\ 2x+5=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-1\\ x=-\frac52\end{array}\right.\)
e: \(4x^2-4x=-1\)
=>\(4x^2-4x+1=0\)
=>\(\left(2x-1\right)^2=0\)
=>2x-1=0
=>2x=1
=>\(x=\frac12\)
f: \(\frac19x^3-x=0\)
=>\(x\left(\frac19x^2-1\right)=0\)
=>\(x\left(x_{}^2-9\right)=0\)
=>x(x-3)(x+3)=0
=>\(\left[\begin{array}{l}x=0\\ x-3=0\\ x+3=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=3\\ x=-3\end{array}\right.\)
g: \(x^3+3x^2+3x=7\)
=>\(x^3+3x^2+3x+1=8\)
=>\(\left(x+1\right)^3=8\)
=>x+1=2
=>x=1