Question

Phân tích thành nhân tử

a) \(x\sqrt{x}+\sqrt{x}-x-1\)

b) \(x-2\sqrt{x-1}-3\)

Answer 1

a)

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

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

= (\(\sqrt{x}-1\) ).( x + 1)

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

Answer 2

b) = x - 1 - 2\(\sqrt{x-1}\) + 1 - 3

= [ ( x - 1) - 2\(\sqrt{x-1}\) + 1 ] - 3

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

= [ \(\left(\sqrt{x-1}-1\right)+\sqrt{3}\) ] . [ \(\left(\sqrt{x}-1\right)-\sqrt{3}\) ]

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

Answer 3

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

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