a: \(\sqrt{x}+\frac{y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\)

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

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

Ta có: \(\frac{x}{\sqrt{xy}+y}+\frac{y}{\sqrt{xy}-x}-\frac{x+y}{\sqrt{xy}}\)

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

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

\(=\frac{x^2-x\sqrt{xy}-y\sqrt{xy}-y^2}{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}-\frac{\left(x+y\right)_{}\left(x-y\right)}{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}\)

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

b: Thay x=3; \(y=4+2\sqrt3\) vào A, ta được:

\(A=\frac{-\left(3+4+2\sqrt3\right)}{3-\left(4+2\sqrt3\right)}=\frac{-7-2\sqrt3}{-2\sqrt3-1}=\frac{7+2\sqrt3}{2\sqrt3+1}\)

\(=\frac{\left(7+2\sqrt3\right)\left(2\sqrt3-1\right)}{12-1}=\frac{14\sqrt3-7+12-2\sqrt3}{11}=\frac{12\sqrt3+5}{11}\)

Có: \(B=x^3-y^3\)

\(B=\left(x-y\right)\left(x^2+xy+y^2\right)\)

Lại có: \(x-y=2\)

\(\Rightarrow\left(x-y\right)^2=4\)

\(\Rightarrow x^2-2xy+y^2=4\)

Mà: \(xy=35\)

\(\Rightarrow x^2-70+y^2=4\)

\(\Rightarrow x^2+y^2=74\)

\(\Rightarrow x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)=2.\left(35+74\right)=2.109=218\)

bạn sửa lại là 9-2t^2 nhé , mình đánh nhầm ^^

chuẩn nhé !

Ta có  ( x + y ) 2 = x 2 + y 2 + 2 x y = 4 − 2 3 = ( 3 − 1 ) 2    ⇒    x + y = 3 − 1.

Suy ra  P = x + y = 3 − 1      k h i     x + y ≥ 0 1 − 3      k h i     x + y < 0 .

What ??!!!

Có x+y=3 rồi tính làm gì nữa

Bạn kia ns đúng á tại mình bấm lộn nút, sorry nha Lê Tài Bảo Châu