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13 tháng 11 2021

\(=\left(x^4+5x^2+2x^3+10x-5x^2-25\right):\left(x^2+5\right)\\ =\left[x^2\left(x^2+5\right)+2x\left(x^2+5\right)-5\left(x^2+5\right)\right]:\left(x^2+5\right)\\ =x^2+2x-5\)

15 tháng 10 2021

\(\dfrac{x^4+2x^3+10x-25}{x^2+5}\)

\(=\dfrac{\left(x^2-5\right)\left(x^2+5\right)+2x\left(x^2+5\right)}{x^2+5}\)

\(=x^2+2x-5\)

22 tháng 7 2018

         \(x^2-5x-4\left(x-5\right)=0\)

\(\Leftrightarrow\)\(x\left(x-5\right)-4\left(x-5\right)=0\)

\(\Leftrightarrow\)\(\left(x-5\right)\left(x-4\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x-5=0\\x-4=0\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=5\\x=4\end{cases}}\)

Vậy....

\(2x\left(x+6\right)=7x+42\)

\(\Leftrightarrow\)\(2x\left(x+6\right)-7x-42=0\)

\(\Leftrightarrow\)\(2x\left(x+6\right)-7\left(x+6\right)=0\)

\(\Leftrightarrow\)\(\left(x+6\right)\left(2x-7\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x+6=0\\2x-7=0\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=-6\\x=\frac{7}{2}\end{cases}}\)

Vậy......

\(x^3-5x^2+x-5=0\)

\(\Leftrightarrow\)\(x^2\left(x-5\right)+\left(x-5\right)=0\)

\(\Leftrightarrow\)\(\left(x-5\right)\left(x^2+1\right)=0\)

\(\Leftrightarrow\)\(x-5=0\)

\(\Leftrightarrow\)\(x=5\)

\(x^4-2x^3+10x^2-20x=0\)

\(\Leftrightarrow\)\(x^3\left(x-2\right)+10x\left(x-2\right)=0\)

\(\Leftrightarrow\)\(x\left(x-2\right)\left(x^2+10\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\\x-2=0\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\\x=2\end{cases}}\)

Vậy...

30 tháng 10 2018

\(\frac{x^4+2x^3+10x-25}{x^2+5}\)

\(=\frac{\left(x^4+5x^2\right)+\left(2x^3+10x\right)-\left(5x^2+25\right)}{x^2+5}\)

\(=\frac{x^2.\left(x^2+5\right)+2x.\left(x^2+5\right)-5.\left(x^2+5\right)}{x^2+5}\)

\(=\frac{\left(x^2+5\right)\left(x^2+2x-5\right)}{x^2+5}\)

\(=x^2+2x-5\)\(\left(x^2+5\ne0\right)\)

Tham khảo nhé~

30 tháng 10 2018

      \(x^4+2x^3+10x-25\)

\(=x^4+5x^2+2x^3+10x-5x^2-25\)

\(=x^2\left(x^2+5\right)+2x\left(x^2+5\right)-5\left(x^2+5\right)\)

\(=\left(x^2+5\right)\left(x^2+2x-5\right)\)

Vậy \(\left(x^4+2x^3+10x-25\right):\left(x^2+5\right)=x^2+2x-5\)

21 tháng 6 2018

Giải:

1) \(\left(x-6\right)\left(x^2+6x+36\right)-\left(x+4\right)^3=\left(x-2\right)^3+\left(x+5\right)\left(x^2-10x+25\right)-\left(2x^3+6x^2\right)\)

\(\Leftrightarrow x^3-216-\left(x^3+12x^2+48x+64\right)=x^3-6x^2+12x-8+x^3+125-2x^3-6x^2\)

\(\Leftrightarrow x^3-216-x^3-12x^2-48x-64=x^3-6x^2+12x-8+x^3+125-2x^3-6x^2\)

\(\Leftrightarrow-280-12x^2-48x=-12x^2+12x+117\)

\(\Leftrightarrow-280-48x-12x-117=0\)

\(\Leftrightarrow-397-60x=0\)

\(\Leftrightarrow-60x=397\)

\(\Leftrightarrow x=-\dfrac{397}{60}\)

Vậy ...

2) \(\left(2x+3\right)^3-\left(2x+5\right)\left(4x^2-10x+25\right)=\left(6x-1\right)^2-\left(x-2\right)\left(x^2+2x+4\right)+x^3\)

\(\Leftrightarrow8x^3+36x^2+54x+27-\left(8x^3+125\right)=36x^2-12x+1-\left(x^3-8\right)+x^3\)

\(\Leftrightarrow8x^3+36x^2+54x+27-8x^3-125=36x^2-12x+1-x^3+8+x^3\)

\(\Leftrightarrow54x-98=-12x+9\)

\(\Leftrightarrow54x+12x=9+98\)

\(\Leftrightarrow66x=107\)

\(\Leftrightarrow x=\dfrac{107}{66}\)

Vậy ...

27 tháng 11 2016

x^4+5x^2-5x^2-25+2x^3+10x

= x^2(x^2+5)-5(x^2+5)+2x(x^2+5)

=(x^2+5)(x^2-5+2x):(x^2+5)

= x^2-5+2x

21 tháng 4 2020

( x+ 2x3 + x - 25 ) : ( x2 +5)