DK \(\hept{\begin{cases}x\ge1\\y\ge1\end{cases}}\)
TH x=y=1 thay vao ta thay thoa man vay {x;y}={1;1} la 1 nghiem
TH x,y khac 1
Xet phuong trinh (1)
\(\sqrt{x-1}+\sqrt{x}\left(3\sqrt{x}-y\right)+x\sqrt{x}=3y+\sqrt{y-1}\)
<=> \(\left(\sqrt{x-1}-\sqrt{y-1}\right)+3x-3y+x\sqrt{x}-y\sqrt{x}=0\)
<=> \(\frac{\left(x-1\right)-\left(y-1\right)}{\sqrt{x-1}+\sqrt{y-1}}+3\left(x-y\right)+\sqrt{x}\left(x-y\right)=0\)
<=> \(\left(x-y\right)\left(\frac{1}{\sqrt{x-1}+\sqrt{y-1}}+3+\sqrt{x}\right)=0\)
<=> x=y ( do cai trong ngoac thu 2 vo nghiem)
the x=y vao phuong trinh (2) duoc
\(3x^3+4=4x^2+3x\)
<=> \(3x^3-4x^2-3x+4=0\)
<=> \(\left(x-1\right)\left(x+1\right)\left(3x-4\right)=0\)
<=> \(\orbr{\begin{cases}x=y=\pm1\\x=y=\frac{4}{3}\end{cases}}\)
Vay {x;y} =....
ket luan nho kiem tra dkxd nha ban, mik quen mat