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i) \(=x\left(x-5\right)+3\left(x-5\right)=\left(x-5\right)\left(x+3\right)\)
j) \(=x\left(x-1\right)+8\left(x-1\right)=\left(x-1\right)\left(x+8\right)\)
k) \(=x\left(x+1\right)+3\left(x+1\right)=\left(x+1\right)\left(x+3\right)\)
l) \(=x\left(x-3\right)-2\left(x-3\right)=\left(x-3\right)\left(x-2\right)\)
m) \(=x\left(x^2-4x+4\right)=x\left(x-2\right)^2\)
\(=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-1-y\right)\left(x-1+y\right)\)
3: \(=\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}=\sqrt{5}-\sqrt{3}\)
4: \(=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}=\sqrt{5}+\sqrt{3}\)
12) \(\sqrt{11+2\sqrt{30}}=\sqrt{\left(\sqrt{6}\right)^2+2.\sqrt{6}.\sqrt{5}+\left(\sqrt{5}\right)^2}\)
\(=\sqrt{\left(\sqrt{6}+\sqrt{5}\right)^2}=\sqrt{6}+\sqrt{5}\)
\(=\sqrt{6+2\cdot\sqrt{6}\cdot\sqrt{5}+5}\)
\(=\sqrt{\left(\sqrt{6}+\sqrt{5}\right)^2}=\sqrt{6}+\sqrt{5}\)
\(\Delta=27^2-4.168=57>0\)
pt có 2 nghiệm pb
\(x=\dfrac{27\pm\sqrt{57}}{2}\)
`x^2-x-2001.2002`
`=x^2-2002x+2001x-2001.2002`
`=x(x-2002)+2001(x-2002)`
`=(x-2002)(x+2001)`.
x2 - x - 2001.2002
= (x2 - 2002x) + (2001x - 2001.2002)
= x(x - 2002) + 2001(x - 2002)
= (x + 2001)(x- 2002)
\(=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)
`4a+1(a<=0=>-a>=0)`
`=1-4(-a)`
`=1-(2sqrt{-a})^2`
`=(1-2sqrt{-a})(1+2sqrt{-a})`
\(a^2+4b^2\)
\(=a^2+4ab+\left(2b\right)^2-4ab\)
\(=\left(a+2b\right)^2-4ab\)
\(=\left(a+2b-2\sqrt{ab}\right)\left(a+2b+2\sqrt{ab}\right)\)