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\(=\left(x\sqrt{x}+y\sqrt{y}\right)+\left(x-y\right)\)
\(=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)+\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)\)
\(=\left(\sqrt{x}+\sqrt{y}\right)\left(x+y-\sqrt{xy}+\sqrt{x}-\sqrt{y}\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x-y-\sqrt{x}-\sqrt{y}\\ =x-y-\left(\sqrt{x}+\sqrt{y}\right)\\ =\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)-\left(\sqrt{x}+\sqrt{y}\right)\\ =\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}-1\right)\)
=(x-y)-(căn x+căn y)
=(căn x-căn y)(căn x+căn y)-(căn x+căn y)
=(căn x+căn y)(căn x-căn y-1)
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Lời giải:
$=x+\sqrt{x}(\sqrt{y}+\sqrt{2})-\sqrt{3}(\sqrt{y}+\sqrt{2})-3$
$=(x-3)+\sqrt{x}(\sqrt{y}+\sqrt{2})-\sqrt{3}(\sqrt{y}+\sqrt{2})$
$=(\sqrt{x}-\sqrt{3})(\sqrt{x}+\sqrt{3})+(\sqrt{y}+\sqrt{2})(\sqrt{x}-\sqrt{3})$
$=(\sqrt{x}-\sqrt{3})(\sqrt{x}+\sqrt{3}+\sqrt{y}+\sqrt{2})$
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\(2+\sqrt{3}+\sqrt{6}+\sqrt{8}=2+\sqrt{3}+\sqrt{6}+2\sqrt{2}\)
\(=2+\sqrt{3}+\sqrt{2}\left(2+\sqrt{3}\right)=\left(2+\sqrt{3}\right)\left(\sqrt{2}+1\right)\)
\(2+\sqrt{3}+\sqrt{6}+\sqrt{8}=\left(\sqrt{2}+1\right)\left(2+\sqrt{3}\right)\)
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Lời giải:
a.
$7-3a=(\sqrt{7}-\sqrt{3a})(\sqrt{7}+\sqrt{3a})$
b.
$14x^2-11=(\sqrt{14}x-\sqrt{11})(\sqrt{14}x+\sqrt{11})$
c.
$3x-6\sqrt{x}-6=3(x-2\sqrt{x}-2)$
$=3[(\sqrt{x}-1)^2-3]$
$=3(\sqrt{x}-1-\sqrt{3})(\sqrt{x}-1+\sqrt{3})$
d.
$x\sqrt{x}-3\sqrt{x}-2=x\sqrt{x}-2x+2x-4\sqrt{x}+\sqrt{x}-2$
$=x(\sqrt{x}-2)+2\sqrt{x}(\sqrt{x}-2)+(\sqrt{x}-2)$
$=(\sqrt{x}-2)(x+2\sqrt{x}+1)$
$=(\sqrt{x}-2)(\sqrt{x}+1)^2$
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\(=\left(\sqrt{x}\right)^3-1^3=\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)
\(x\sqrt{x}-1=\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)
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a) \(A=\left(\sqrt{x}+3\right)^2-4\sqrt{x}-6\)
\(A=x+6\sqrt{x}+9-4\sqrt{x}-6\)
\(A=x+2\sqrt{x}-3\)
b) \(A=x+2\sqrt{x}-3\)
\(A=x+3\sqrt{x}-\sqrt{x}-3\)
\(A=\sqrt{x}\left(\sqrt{x}+3\right)-\left(\sqrt{x}+3\right)\)
\(A=\left(\sqrt{x}-3\right)\left(\sqrt{x}-1\right)\)
a: A=x+6căn x+9-4căn x-6
=x+2căn x+3
b: A ko phân tích được nha bạn
\(x+\sqrt{x}-2=\left(\sqrt{x}\right)^2-\sqrt{x}+2\sqrt{x}-2\)
\(=\sqrt{x}\left(\sqrt{x}-1\right)+2\left(\sqrt{x}-1\right)\)
\(=\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\)
\(x+\sqrt{x}-2=\left(x-\sqrt{x}\right)+\left(2\sqrt{x}-2\right)\)
\(=\sqrt{x}\left(\sqrt{x}-1\right)+2\left(\sqrt{x}-1\right)=\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\)