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1,\(x^4-x=0\\ ->x\left(x-1\right)\left(x^2+x+1\right)=0\\ ->\left(......\right)\)
2\(x^4-x^2=0\\ ->x^2\left(x^2-1\right)\\ ->x^2\left(x-1\right)\left(x+1\right)\\ ->......\)
3,\(x^5+x^2\\ ->x^2\left(x^3+1\right)\\ ->x^2\left(x+1\right)\left(x^2-x+1\right)\\ ->.......\)
4\(3x\left(x-20\right)-x+20=0->\left(3x-1\right)\left(x-20\right)=0->.....\)
b, x = -5/3 hoặc x = 4/3.
c, x = 0 hoặc x = 3, -3.
d, x = 0 hoặc x = 2, -2.
e, x = 1 hoặc x = \(\dfrac{-1}{2}\).
a: \(\Leftrightarrow x^2-40x+400-x^2-4x-3=-7\)
=>-44x+397=-7
=>-44x=-404
hay x=101
b: \(\Leftrightarrow\left[{}\begin{matrix}3x+5=0\\4-3x=0\end{matrix}\right.\Leftrightarrow x\in\left\{-\dfrac{5}{3};\dfrac{4}{3}\right\}\)
c: \(\Leftrightarrow x\left(x^2-9\right)=0\)
=>x(x-3)(x+3)=0
hay \(x\in\left\{0;3;-3\right\}\)
d: \(\Leftrightarrow x\left(x-2\right)\left(x+2\right)=0\)
hay \(x\in\left\{0;2;-2\right\}\)
e: =>(2x+1)(1-x)=0
=>x=-1/2 hoặc x=1
a. Ta có: \(x^2-10x+26+y^2+2y=0\Leftrightarrow\left(x^2-10x+25\right)+\left(y^2+2y+1\right)=0\\ \)
\(\Leftrightarrow\left(x+5\right)^2+\left(y+1\right)^2=0\Rightarrow\hept{\begin{cases}x+5=0\\y+1=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=-5\\y=-1\end{cases}}}\)
b. \(\left(2x+5\right)^2-\left(x-7\right)^2=0\Leftrightarrow\left(2x+5+x-7\right).\left(2x+5-x+7\right)=0\)
\(\Leftrightarrow\left(3x-2\right).\left(x+12\right)=0\Leftrightarrow\orbr{\begin{cases}3x-2=0\\x+12=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{2}{3}\\x=-12\end{cases}}}\)
c. \(25.\left(x-3\right)^2=49.\left(1-2x\right)^2\Leftrightarrow\left(5x-15\right)^2=\left(7-14x\right)^2\Leftrightarrow\left(5x-15\right)^2-\left(7-14x\right)^2=0\)
\(\Leftrightarrow\left(5x-15-7+14x\right).\left(5x-15+7-14x\right)=0\Leftrightarrow\left(19x-22\right).\left(-9x-8\right)=0\)
\(\Leftrightarrow\left(19x-22\right).\left(9x+8\right)=0\Leftrightarrow\orbr{\begin{cases}19x-22=0\\9x+8=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{22}{19}\\x=-\frac{8}{9}\end{cases}}}\)
d. \(\left(x+2\right)^2=\left(3x-5\right)^2\Leftrightarrow\left(x+2\right)^2-\left(3x-5\right)^2=0\Leftrightarrow\left(x+2+3x-5\right).\left(x+3-3x+5\right)=0\)
\(\Leftrightarrow\left(4x-3\right).\left(8-2x\right)=0\Leftrightarrow\orbr{\begin{cases}4x-3=0\\8-2x=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{3}{4}\\x=4\end{cases}}}\)
e. \(x^2-2x+1=16\Leftrightarrow\left(x-1\right)^2-16=0\Leftrightarrow\left(x-1-4\right).\left(x-1+4\right)=0\)
\(\Leftrightarrow\left(x-5\right).\left(x+3\right)=0\Leftrightarrow\orbr{\begin{cases}x-5=0\\x+3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=5\\x=-3\end{cases}}}\)
1) \(-6x^2-x+7=0\)
\(\Leftrightarrow-6x^2+6x-7x+7=0\)
\(\Leftrightarrow\left(-6x^2+6x\right)-\left(7x-7\right)=0\)
\(\Leftrightarrow-6x\left(x-1\right)-7\left(x-1\right)=0\)
\(\Leftrightarrow\left(-6x-7\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-6x-7=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{7}{6}\\x=1\end{matrix}\right.\)
2) \(-4x^2-5x+9=0\)
\(\Leftrightarrow-4x^2+4x-9x+9=0\)
\(\Leftrightarrow\left(-4x^2+4x\right)-\left(9x-9\right)=0\)
\(\Leftrightarrow-4x\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow\left(-4x-9\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-4x-9=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{9}{4}\\x=1\end{matrix}\right.\)
3) \(x^2+3x-4=0\)
\(\Leftrightarrow x^2-x+4x-4=0\)
\(\Leftrightarrow\left(x^2-x\right)+\left(4x-4\right)=0\)
\(\Leftrightarrow x\left(x-1\right)+4\left(x-1\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=1\end{matrix}\right.\)
4) \(x^2-6x-7=0\)
\(\Leftrightarrow x^2+x-7x-7=0\)
\(\Leftrightarrow\left(x^2+x\right)-\left(7x+7\right)=0\)
\(\Leftrightarrow x\left(x+1\right)-7\left(x+1\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=-1\end{matrix}\right.\)
5) \(x^2+5x+4=0\)
\(\Leftrightarrow x^2+x+4x+4=0\)
\(\Leftrightarrow\left(x^2+x\right)+\left(4x+4\right)=0\)
\(\Leftrightarrow x\left(x+1\right)+4\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-1\end{matrix}\right.\)
a) \(-6x^2-x+7=0\)
\(\Leftrightarrow-6x^2+6x-7x+7=0\)
\(\Leftrightarrow-6x\left(x-1\right)-7\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(-6x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{-7}{6}\end{matrix}\right.\)
b) \(-4x^2-5x+9=0\)
\(\Leftrightarrow-4x^2+4x-9x+9=0\)
\(\Leftrightarrow-4x\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(-4x-9\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2,25\end{matrix}\right.\)
c) \(x^2+3x-4=0\)
\(\Leftrightarrow x^2-x+4x-4=0\)
\(\Leftrightarrow x\left(x-1\right)+4\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-4\end{matrix}\right.\)
d) \(x^2-6x-7=0\)
\(\Leftrightarrow x^2+x-7x-7=0\)
\(\Leftrightarrow x\left(x+1\right)-7\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=7\end{matrix}\right.\)
e) \(x^2+5x+4=0\)
\(\Leftrightarrow x^2+x+4x+4=0\)
\(\Leftrightarrow x\left(x+1\right)+4\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-4\end{matrix}\right.\)
1: \(\Leftrightarrow3x+4x=4\)
=>7x=4
hay x=4/7
2: \(\Leftrightarrow3x-5x-5^3:5^2=0\)
=>-2x=5
=>x=-5/2
a: \(x\in\left\{0;25\right\}\)
c: \(x\in\left\{0;5\right\}\)
a) \(\Leftrightarrow\left(-63x^2+78x-15\right)+\left(63x^3+x-20\right)=44\)
\(\Leftrightarrow-63x^2+78x-15+63x^2+x-20=44\)
\(\Leftrightarrow79x-35=44\)
\(\Leftrightarrow79x=44+35\)
\(\Leftrightarrow79x=79\)
\(\Leftrightarrow x=1\)
b) \(\Leftrightarrow\left(x^2+3x+2\right).\left(x+5\right)-x^2.\left(x+8\right)=27\)
\(\Leftrightarrow x.\left(x^2+3x+2\right)+5.\left(x^2+3x+2\right)-x^3-8x^2=27\)
\(\Leftrightarrow x^3+3x^2+2x+5x^2+15x+10-x^3-8x^2=27\)
\(\Leftrightarrow17x+10=27\)
\(\Leftrightarrow17x=17\)
\(\Leftrightarrow x=1\)
1: =>3x(x-20)-(x-20)=0
=>(x-20)(3x-1)=0
=>x=1/3 hoặc x=20
3: \(\Leftrightarrow x^2\left(x^3+1\right)=0\)
=>x=0 hoặc x=-1
4: \(\Leftrightarrow x\left(x-3\right)-3\left(x-3\right)=0\)
=>(x-3)2=0
=>x=3