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7 tháng 12 2023

\(x\sqrt{x}+2x+\sqrt{x}+2\left(x>0\right)\)

\(=\left(x\sqrt{x}+\sqrt{x}\right)+\left(2x+2\right)\)

\(=\sqrt{x}\left(x+1\right)+2\left(x+1\right)\)

\(=\left(\sqrt{x}+2\right)\left(x+1\right)\)

\(x-\sqrt{x}-6=\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)\)

\(2x+5\sqrt{x}-3=\left(\sqrt{x}+3\right)\left(2\sqrt{x}-1\right)\)

11 tháng 7 2021

\(2+\sqrt{3}+\sqrt{6}+\sqrt{8}=2+\sqrt{3}+\sqrt{6}+2\sqrt{2}\)

\(=2+\sqrt{3}+\sqrt{2}\left(2+\sqrt{3}\right)=\left(2+\sqrt{3}\right)\left(\sqrt{2}+1\right)\)

\(2+\sqrt{3}+\sqrt{6}+\sqrt{8}=\left(\sqrt{2}+1\right)\left(2+\sqrt{3}\right)\)

NV
11 tháng 7 2021

\(=\left(\sqrt{x}\right)^3-1^3=\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)

\(x\sqrt{x}-1=\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)

11 tháng 9 2021

\(x+2\sqrt{x-1}=\left(x-1\right)+2\sqrt{x-1}+1=\left(\sqrt{x-1}+1\right)^2\)

\(x-4\sqrt{x-2}+2=\left(x-2\right)-4\sqrt{x-2}+4=\left(\sqrt{x-2}-2\right)^2\)

\(x+2\sqrt{x-1}=\left(\sqrt{x-1}+1\right)^2\)

\(x-4\sqrt{x-2}+2=\left(\sqrt{x-2}+4\right)^2\)

21 tháng 8 2018

\(2x^2-3x\sqrt{x+3}+\left(x+3\right)\)

\(=2x^2-2x\sqrt{x+3}-x\sqrt{x+3}+\left(\sqrt{x+3}\right)^2\)

\(=2x\left(x-\sqrt{x+3}\right)-\sqrt{x+3}\left(x-\sqrt{x+3}\right)\)

\(=\left(2x-\sqrt{x+3}\right)\left(x-\sqrt{x+3}\right)\)

21 tháng 8 2018

\(2x^2-3x\sqrt{x+3}+\left(x+3\right)\)

\(=2x^2-x\sqrt{x+3}-2x\sqrt{x+3}+\left(\sqrt{x+3}\right)^2\)

\(=x\left(2x-\sqrt{x+3}\right)-\sqrt{x+3}\left(2x-\sqrt{x+3}\right)\)

\(=\left(x-\sqrt{x+3}\right)\left(2x-\sqrt{x+3}\right)\)

a) \(x-1=\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)

b) \(x-\sqrt{x}-2=\left(\sqrt{x}-2\right)\cdot\left(\sqrt{x}+1\right)\)

c) \(x\sqrt{x}+1=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)

4 tháng 7 2021

\(a.x-1=\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\\ b.x-\sqrt{x}-2=\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)\\ c.x\sqrt{x}+1=\sqrt{x^3}+\sqrt{1^3}=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)

d: \(=-\left(x+\sqrt{x}-12\right)=-\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)\)

14 tháng 8 2020

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

                            \(=\sqrt{x}\left(\sqrt{x}-1\right)+2\left(\sqrt{x}-1\right)\)

                            \(=\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\)

                          

14 tháng 8 2020

\(x+\sqrt{x}-2=\left(x-\sqrt{x}\right)+\left(2\sqrt{x}-2\right)\)

\(=\sqrt{x}\left(\sqrt{x}-1\right)+2\left(\sqrt{x}-1\right)=\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\)