\(\left\{{}\begin{matrix}x^3-y^3-9=0\\6x^2-12x+3y^2+3y=0\end{matrix}\right.\)
\(\Rightarrow x^3-6x^2+12x-8-\left(y^3+3y^2+3y+1\right)=0\)
\(\Leftrightarrow\left(x-2\right)^3=\left(y+1\right)^3\)
\(\Leftrightarrow x-2=y+1\Rightarrow y=x-3\)
Thế vào pt dưới:
\(2x^2+\left(x-3\right)^2-4x+x-3=0\)
\(\Leftrightarrow...\)
b/ ĐKXĐ: \(x;y\ge1\)
Trừ trên cho dưới:
\(\Rightarrow2\left(\sqrt{x^2+5}-\sqrt{y^2+5}\right)+2\left(\sqrt{x-1}-\sqrt{y-1}\right)+x^2-y^2=0\)
\(\Leftrightarrow\frac{\left(x-y\right)\left(2x+2y\right)}{\sqrt{x^2+5}+\sqrt{y^2+5}}+\frac{2\left(x-y\right)}{\sqrt{x-1}+\sqrt{y-1}}+\left(x-y\right)\left(x+y\right)=0\)
\(\Leftrightarrow\left(x-y\right)\left(\frac{2x+2y}{\sqrt{x^2+5}+\sqrt{y^2+5}}+\frac{2}{\sqrt{x-1}+\sqrt{y-1}}+x+y\right)=0\)
\(\Leftrightarrow x-y=0\Rightarrow x=y\)
Thay vào pt đầu:
\(2\sqrt{x^2+5}=2\sqrt{x-1}+x^2\)
\(\Leftrightarrow x^2+2-2\sqrt{x^2+5}+2\left(\sqrt{x-1}-1\right)=0\)
\(\Leftrightarrow\frac{x^4-16}{x^2+2+2\sqrt{x^2+5}}+\frac{2\left(x-2\right)}{\sqrt{x-1}+1}=0\)
\(\Leftrightarrow\frac{\left(x-2\right)\left(x+2\right)\left(x^2+4\right)}{x^2+2+2\sqrt{x^2+5}}+\frac{2\left(x-2\right)}{\sqrt{x-1}+1}=0\)
\(\Leftrightarrow\left(x-2\right)\left(\frac{\left(x+2\right)\left(x^2+4\right)}{x^2+2+2\sqrt{x^2+5}}+\frac{2}{\sqrt{x-1}+1}\right)=0\)
\(\Rightarrow x=y=2\)
