\(x\sqrt{y}-y\sqrt{x}=\sqrt{x^2}.\sqrt{y}-\sqrt{y^2}.\sqrt{x}=\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)\)

\(x\sqrt{y}-y\sqrt{x}=\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)\)

`x \sqrt{y} - y \sqrt{x}`

`= (\sqrt{x})^2 . \sqrt{y} - (\sqrt{y})^2 . \sqrt{x}`

`= \sqrt{x} . \sqrt{y} . (\sqrt{x} - \sqrt{y})`

`= \sqrt{xy} . (\sqrt{x} - \sqrt{y})`

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

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

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

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

x - 3 = ( √x )² - ( √3 )² = ( √x - √3 )( √x + √3 ) < với x > 0 >

            Bài làm :

Ta có :

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

\(\sqrt{x}+\sqrt{y}+\sqrt{xy}+1\)

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

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

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

( căn x + 1 ) + ( căn y + căn xy )
( căn x + 1 ) + căn y.( căn x +  1)
( căn x +1 )(căn y + 1 )

#)Giải :

\(x^3-2x-4\)

\(=x^3+2x^2-2x^2+2x-4x-4\)

\(=x^3+2x^2+2x-2x^2-4x-4\)

\(=x\left(x^2+2x+2\right)-2\left(x^2+2x+2\right)\)

\(=\left(x-2\right)\left(x^2+2x+2\right)\)

\(x^4+2x^3+5x^2+4x-12\)

\(=x^4+x^3+6x^2+x^3+x^2+6x-2x^2-2x-12\)

\(=x^2\left(x^2+x+6\right)+x\left(x^2+x+6\right)-2\left(x^2+x+6\right)\)

\(=\left(x^2+x+6\right)\left(x^2+x-2\right)\)

\(=\left(x^2+x+6\right)\left(x-1\right)\left(x+2\right)\)

Câu 1.

Đoán được nghiệm là 2.Ta giải như sau:

\(x^3-2x-4\)

\(=x^3-2x^2+2x^2-4x+2x-4\)

\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)

\(=\left(x-2\right)\left(x^2+2x+2\right)\)

cảm ơn nha!

\(x^2-x-12\\ =x^2-4x+3x-12\\ =x\left(x-4\right)+3\left(x-4\right)\\ =\left(x-4\right)\left(x+3\right)\)

\(x^3-x-12\)

\(=x^3-4x+3x-12\)

\(=x\left(x^2-4\right)+3\left(x-4\right)\)

\(=x\left(x-4\right)\left(x+4\right)+3\left(x-4\right)\)

\(=\left(x-4\right)\left[x\left(x+4\right)+3\right]\)

\(=\left(x-4\right)\left(x^2+4x+3\right)\)