Tìm x
(8-5x)(x+2)+4(x-2)(x+1)+2(x-2)(x+2)=0
4(x-1)(x+5)-(x+2)(x+5)=3(x-1)(x+2)
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1) Ta có: \(3\left(x-1\right)-5\left(x-2\right)=4\left(x+1\right)\)
\(\Leftrightarrow3x-5-5x+10-4x-4=0\)
\(\Leftrightarrow-6x+1=0\)
\(\Leftrightarrow-6x=-1\)
hay \(x=\dfrac{1}{6}\)
2) Ta có: \(-2\left(x-2\right)-4\left(x+1\right)=-3\left(x+3\right)\)
\(\Leftrightarrow-2x+4-4x-4+3x+9=0\)
\(\Leftrightarrow-3x=-9\)
hay x=3
3) Ta có: \(3x^2+2x=0\)
\(\Leftrightarrow x\left(3x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{2}{3}\end{matrix}\right.\)
4) Ta có: \(x^2-5x=0\)
\(\Leftrightarrow x\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\)
5) Ta có: \(\left(2x-3\right)^2=36\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=6\\2x-3=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=9\\2x=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\)
6) Ta có: \(\left(5x-1\right)^3=125\)
\(\Leftrightarrow5x-1=5\)
\(\Leftrightarrow5x=6\)
hay \(x=\dfrac{6}{5}\)
7) Ta có: \(3^{x+1}=27\)
\(\Leftrightarrow x+1=3\)
hay x=2
Bạn nên viết lại đề bài cho sáng sủa, rõ ràng để người đọc dễ hiểu hơn.
f: =>4(x^2+4x-5)-x^2-7x-10=3(x^2+x-2)
=>4x^2+16x-20-x^2-7x-10-3x^2-3x+6=0
=>6x-24=0
=>x=4
e: =>8x+16-5x^2-10x+4(x^2-x-2)=4-x^2
=>-5x^2-2x+16+4x^2-4x-8=4-x^2
=>-6x+8=4
=>-6x=-4
=>x=2/3
d: =>2x^2+3x^2-3=5x^2+5x
=>5x=-3
=>x=-3/5
b: =>2x^2-8x+3x-12+x^2-7x+10=3x^2-12x-5x+20
=>-12x-2=-17x+20
=>5x=22
=>x=22/5
Lời giải:
a. $2x^2+3(x-1)(x+1)=5x(x+1)$
$\Leftrightarrow 2x^2+3x^2-3=5x^2+5x$
$\Leftrightarrow 5x^2-3=5x^2+5x$
$\Leftrightarrow 5x=-3$
$\Leftrightarrow x=\frac{-3}{5}$
b.
PT $\Leftrightarrow (-5x^2-2x+16)+4(x^2-x-2)=4-x^2$
$\Leftrightarrow -x^2-6x+8=4-x^2$
$\Leftrightarrow -6x+8=4$
$\Leftrightarrow -6x=-4$
$\Leftrightarrow x=\frac{2}{3}$
c.
PT $\Leftrightarrow 4(x^2+4x-5)-(x^2+7x+10)=3(x^2+x-2)$
$\Leftrightarrow 4x^2+16x-20-x^2-7x-10=3x^2+3x-6$
$\Leftrightarrow 3x^2+9x-30=3x^2+3x-6$
$\Leftrightarrow 6x=24$
$\Leftrightarrow x=4$
<=> 2(x^2-25) - 2x^2+3x-4x+6 + x^3-8x = x^3+1
=>2x^2-50 - 2x^2 -9x+6+x^3-x^3-1 = 0
<=>-9x - 45 =0
<=>-9x=45
<=>x=-5
Còn phần b và c bạn cứ khai triển ra,mình phải đi học nên không có thời gian giải cho bạn
\(a.\left(x-2\right)^2-\left(x+3\right)^2-4\left(x+1\right)=5\)
\(\left(x^2-4x+4\right)-\left(x^2+6x+9\right)-4x-4=5\)
\(\left(-4x-6x\right)+\left(4-9\right)-4x-4=5\)
\(-10x-5-4x-4=5\)
\(-14x-9=5\)
\(-14x=14\Rightarrow x=-1\)
\(b.\left(2x-3\right)\left(2x+3\right)-\left(x-1\right)^2-3x\left(x-5\right)=-44\)
\(4x^2-9-\left(x^2-2x+1\right)-\left(3x^2-15x\right)=-44\)
\(4x^2-9-x^2+2x-1-3x^2+15x=-44\)
\(17x-10=-44\)
\(17x=-34\Rightarrow x=-2\)
\(c.\left(5x+1\right)^2-\left(5x-3\right)\left(5x+3\right)=30\)
\(25x^2+10x+1-\left(25x^2-9\right)=30\)
\(10x+10=30\)
\(10x=20\Rightarrow x=2\)
\(d.\left(x+3\right)^2+\left(x-2\right)\left(x+2\right)-2\left(x-1\right)^2=7\)
\(\left(x^2+6x+9\right)+\left(x^2-4\right)-2\left(x^2-2x+1\right)=7\)
\(2x^2+6x+5-2x^2+4x-2=7\)
\(10x+3=7\)
\(10x=4\Rightarrow x=\frac{4}{10}=\frac25\)
\(f.\left(3x-8\right)^2=0\)
\(3x-8=0\Rightarrow x=\frac83\)
\(e.6\left(x+1\right)^2-2\left(x+1\right)+2\left(x-1\right)\left(x^2+x+1\right)=0\)
\(6\left(x^2+2x+1\right)-2x-2+2\left(x^3-1\right)=0\)
\(6x^2+12x+6-2x-2+2x^3-2=0\)
\(2x^3+6x^2+10x+2=0\)
\(\Rightarrow x\approx-0,23\)
b: =>2x^2-8x+3x-12+x^2-7x+10=3x^2-17x+20
=>-12x-2=-17x+20
=>5x=22
=>x=22/5
c: =>24x^2+16x-9x-6-4x^2-16x-7x-28=20x^2-4x+5x-1
=>-16x-34=x-1
=>-17x=33
=>x=-33/17
d: =>2x^2+3x^2-3=5x^2+5x
=>5x=-3
=>x=-3/5
e: =>8x+16-5x^2-10x+4x^2-4x-8=4-x^2
=>-6x+8=4
=>-6x=-4
=>x=2/3
f: =>4(x^2+4x-5)-x^2-7x-10=3x^2+3x-6
=>4x^2+16x-20-4x^2-10x+4=0
=>6x=16
=>x=8/3