Question

[Hằng Trần]

Giải giúp mình vs ><

1/ Thực hiện phép tính

a)\(\sqrt{9-2\sqrt{20}}+\sqrt{12-2\sqrt{35}}\)

b)\(\sqrt{5-\sqrt{21}}-\sqrt{5+\sqrt{21}}\)

2/ Rút gọn biểu thức

a) \(\sqrt{\dfrac{\left(x-2\right)^4}{\left(3-x\right)^2}}+\dfrac{x^2-1}{x-3}\) (x < 3)

b) \(4x-\sqrt{8}+\dfrac{\sqrt{x^3+2x^2}}{\sqrt{x+2}}\) (x > -2)

3/ Phân tích thành nhân tử

a) \(\sqrt{x}+\sqrt{y}-5\sqrt{xy}-5y\left(x,y\ge0\right)\)

b) \(x\sqrt{x}-y\sqrt{y}\left(x,y\ge0\right)\)

Answer 1

[DƯƠNG PHAN KHÁNH DƯƠNG]

Bài 1 : Thực hiện phép tính :

a ) \(\sqrt{9-2\sqrt{20}}+\sqrt{12-2\sqrt{35}}\)

\(=\sqrt{5-2\sqrt{20}+4}+\sqrt{7-2\sqrt{35}+5}\)

\(=\sqrt{\left(\sqrt{5}-2\right)^2}+\sqrt{\left(\sqrt{7}-\sqrt{5}\right)}^2\)

\(=\sqrt{5}-2+\sqrt{7}-\sqrt{5}\)

\(=\sqrt{7}-2\)

b ) \(\sqrt{5-\sqrt{21}}-\sqrt{5+\sqrt{21}}\)

\(=\sqrt{\dfrac{2\left(5-\sqrt{21}\right)}{2}}-\sqrt{\dfrac{2\left(5+\sqrt{21}\right)}{2}}\)

\(=\sqrt{\dfrac{10-2\sqrt{21}}{2}}-\sqrt{\dfrac{10+2\sqrt{21}}{2}}\)

\(=\dfrac{\sqrt{7-2\sqrt{21}+3}}{\sqrt{2}}-\dfrac{\sqrt{7+2\sqrt{21}+3}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}}{\sqrt{2}}-\dfrac{\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{2}}-\dfrac{\sqrt{7}+\sqrt{3}}{\sqrt{2}}\)

\(=\dfrac{-2\sqrt{3}}{\sqrt{2}}=-\sqrt{6}\)

Answer 2

[Hằng Trần]

giúp mình mấy câu còn lại vs bạn ơi