2k6 thì dạng này EZ quá còn gì:)

\(\sqrt{x}\left(\sqrt{x}+\sqrt{y}\right)=3\sqrt{y}\left(\sqrt{x}+5\sqrt{y}\right)\)

\(\Leftrightarrow x+\sqrt{xy}-3\sqrt{xy}-15y=0\)

\(\Leftrightarrow x-2\sqrt{xy}-15y=0\Leftrightarrow\left(\sqrt{x}-5\sqrt{y}\right)\left(\sqrt{x}+3\sqrt{y}\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}\sqrt{x}-5\sqrt{y}=0\\\sqrt{x}+3\sqrt{y}=0\end{cases}}\Leftrightarrow\sqrt{x}=5\sqrt{y}\Leftrightarrow x=25y\)

Khi đó : \(E=\frac{2x+\sqrt{xy}+3y}{x+\sqrt{xy}-y}=\frac{50y+5y+3y}{25y+5y-y}=\frac{58y}{29y}=2\)

(3*x-1)*y+2*căn bậc hai(x)*y+2*x

ĐKXĐ : x;y > 0

\(\sqrt{x}\left(\sqrt{x}+\sqrt{y}\right)=3\sqrt{y}\left(\sqrt{x}+5\sqrt{y}\right)\)

\(\Leftrightarrow x+\sqrt{xy}=3\sqrt{xy}+15y\)

\(\Leftrightarrow x=2\sqrt{xy}+15y\)

\(\Leftrightarrow\left(x-2\sqrt{xy}+y\right)-16y=0\)

\(\Leftrightarrow\left(\sqrt{x}-\sqrt{y}\right)^2-\left(4\sqrt{y}\right)^2=0\)

\(\Leftrightarrow\left(\sqrt{x}-5\sqrt{y}\right)\left(\sqrt{x}+3\sqrt{y}\right)=0\)

Mà theo đk x;y > 0 nên \(\sqrt{x}+3\sqrt{y}>0\) Do đó \(\sqrt{x}-5\sqrt{y}=0\Rightarrow\sqrt{x}=5\sqrt{y}\Rightarrow x=25y\)

Thay vào C ta được :

\(C=\frac{2.25y+\sqrt{25y.y}+3y}{25y+\sqrt{25y.y}-y}=\frac{50y+5y+3y}{25y+5y-y}=2\)

Đặt \(\left\{{}\begin{matrix}\sqrt{2x+3}=a\ge0\\\sqrt{y}=b\ge0\end{matrix}\right.\)

\(\Rightarrow b\left(b^2+1\right)-3a^2=\left(a^2+1\right)a-3b^2\)

\(\Rightarrow a^3-b^3+3a^2-3b^2+a-b=0\)

\(\Leftrightarrow\left(a-b\right)\left(a^2+ab+b^2\right)+\left(a-b\right)\left(3a+3b\right)+a-b=0\)

\(\Leftrightarrow\left(a-b\right)\left(a^2+ab+b^2+3a+3b+1\right)=0\)

\(\Leftrightarrow a=b\Rightarrow\sqrt{2x+3}=\sqrt{y}\)

\(\Rightarrow y=2x+3\)

\(\Rightarrow M=x\left(2x+3\right)+3\left(2x+3\right)-4x^2-3\) tới đây chắc chỉ cần bấm máy

B=3,406938828

xcănx=cănx mũ 3

y căn y = căn y mũ 3