Question

Nghỉ mấy ngày mà btvn toàn hệ :)) ai giúp cái đi @@

\(\hept{\begin{cases}\sqrt{x-1}+\sqrt{x}\left(3\sqrt{x}-y\right)+x\sqrt{x}=3y+\sqrt{y-1}\\3xy^2+4=4x^2+2y+x\end{cases}}\)

Answer 1

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} =....

Answer 2

ket luan nho kiem tra dkxd nha ban, mik quen mat

Answer 3

Tks bn nhé @@