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\(x-\sqrt{x}-6=\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)\)
\(2x+5\sqrt{x}-3=\left(\sqrt{x}+3\right)\left(2\sqrt{x}-1\right)\)
\(3\left(x-1\right)^2-3x\left(x-5\right)=1\)
⇔ \(3\left(x^2-2x+1\right)-3x\left(x-5\right)=1\)
⇔ \(3x^2-6x+3-3x^2+15x=1\)
⇔ \(9x+3=1\)
⇔ \(9x=1-3\)
⇔ \(9x=-2\)
⇔ \(x=\dfrac{-2}{9}\)
b, <=>(4x)3+13
<=> (4x+1)( 16x2-4x+1)
c, <=> (x.y2.z3)3-53
<=> (xy2z3-5)( x2y4z6+5xy2z3+25)
d, <=> (3x2)3-(2x)3
<=> (3x2-2x)(9x4+6x3+4x2)
d, (x3)2- (y3)2
= (x3+y3)(x3-y3)
\(=\dfrac{\sqrt{3}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}-\sqrt{6}-3-\sqrt{6}\)
=căn 3-2căn 6-3
\(2x^2-3x\sqrt{x+3}+\left(x+3\right)\)
\(=2x^2-2x\sqrt{x+3}-x\sqrt{x+3}+\left(\sqrt{x+3}\right)^2\)
\(=2x\left(x-\sqrt{x+3}\right)-\sqrt{x+3}\left(x-\sqrt{x+3}\right)\)
\(=\left(2x-\sqrt{x+3}\right)\left(x-\sqrt{x+3}\right)\)
\(2x^2-3x\sqrt{x+3}+\left(x+3\right)\)
\(=2x^2-x\sqrt{x+3}-2x\sqrt{x+3}+\left(\sqrt{x+3}\right)^2\)
\(=x\left(2x-\sqrt{x+3}\right)-\sqrt{x+3}\left(2x-\sqrt{x+3}\right)\)
\(=\left(x-\sqrt{x+3}\right)\left(2x-\sqrt{x+3}\right)\)
\(2x-7\sqrt{x}+3\\ =2x-6\sqrt{x}-\sqrt{x}+3\\ =\left(2x-6\sqrt{x}\right)-\left(\sqrt{x}-3\right)\\ =2\sqrt{x}\left(\sqrt{x}-3\right)-\left(\sqrt{x}-3\right)\\ =\left(\sqrt{x}-3\right)\left(2\sqrt{x}-1\right)\)
=2x-6căn x-căn x+3
=2*căn x*(căn x-3)-(căn x-3)
=(căn x-3)(2*căn x-1)