Bài 2:
a: =>5x(1-3x)=0
=>x=0 hoặc x=1/3
b: =>x^2-6x+9=0
=>(x-3)^2=0
=>x-3=0
=>x=3
Bài 4:
a: \(=x^4+2x^2+1-2x^2\)
\(=\left(x^2+1\right)^2-2x^2\)
\(=\left(x^2-x\sqrt{2}+1\right)\left(x^2+x\sqrt{2}+1\right)\)
b: \(=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)
`1)`
`a)(a+5)^2+2(a+5)(1/2-a)+(1/2-a)^2`
`=(a+5+1/2-a)^2=(11/2)^2=121/4`
~~~~~~~~~~~~
`b)[x^2-16+2xy+y^2]/[3x^2-12x+3xy]` `ĐK: x \ne 0,x \ne 4-y`
`=[(x+y)^2-4^2]/[3x(x-4+y)]`
`=[(x+y-4)(x+y+4)]/[3x(x+y-4)]`
`=[x+y+4]/[3x]`
_______________________________________________________
`2)`
`a)5x-15x^2=0`
`<=>5x(1-3x)=0`
`<=>[(x=0),(x=1/3):}`
~~~~~~~~~~~
`b)x^2+9=6x`
`<=>x^2-6x+9=0`
`<=>(x-3)^2=0`
`<=>x=3`
_______________________________________________________
`3)(2x^3-7x^2+7x-2):(x-2)`
`=(2x^3-4x^2-3x^2+6x+x-2):(x-2)`
`=(x-2)(2x^2-3x+1):(x-2)`
`=2x^2-3x+1`
_______________________________________________________
`4)`
`a)x^4+1`
`=x^4+2x^2+1-2x^2`
`=(x^2+1)^2-2x^2`
`=(x^2+1-\sqrt{2}x)(x^2+1+\sqrt{2}x)`
~~~~~~~~~~~
`b)4x^4+81`
`=4x^4+36x^2+81-36x^2`
`=(2x^2+9)-36x^2`
`=(2x^2+9-6x)(2x^2+9+6x)`
`1.`
`a.`\(\left(a+5\right)^2+2\left(a+5\right)\left(\dfrac{1}{2}-a\right)+\left(1-a\right)^2\)
\(=\left(a+5+1-a\right)^2\)
\(=6^2=36\)
`b.`\(\dfrac{x^2-16+2xy+y^2}{3x^2-12x+3xy}\)
\(=\dfrac{\left(x+y\right)^2-16}{3x\left(x-4+y\right)}\)
\(=\dfrac{\left(x+y-4\right)\left(x+y+4\right)}{3x\left(x+y-4\right)}\)
\(=\dfrac{x+y+4}{3x}\)
`2.`
`a.`\(5x-15x^2=0\)
`<=>5x(1-3x)=0`
\(\Leftrightarrow\left[{}\begin{matrix}5x=0\\1-3x=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{3}\end{matrix}\right.\)
`b.x^2+9=6x`
`<=>x^2-6x+9=0`
`<=>(x-3)^2=0`
`<=>x-3=0`
`<=>x=3`
`3.`\(\dfrac{2x^3-7x^2+7x-2}{x-2}=2x^2-3x+1\)
`4.`
`a.x^4+1`
`=(x^2)^2+1`
`b.4x^4+81`
`=(2x^2)^2+9^2`
