Question

[ngu ngoc linh]

Giải hệ Phương trình {_{7x³+11=3(x+y)(x+y+1)}^xy(3x+y)=4

Answer 1

[Đoàn Đức Hà]

\(7x^3+11=3\left(x+y\right)\left(x+y+1\right)\)

\(\Leftrightarrow\left(x+y\right)^3+7x^3+11+1=\left(x+y\right)^3+3\left(x+y\right)\left(x+y+1\right)+1\)

\(\Leftrightarrow x^3+3x^2y+3xy^2+y^3+7x^3+3xy\left(3x+y\right)=\left(x+y\right)^3+3\left(x+y\right)^2+3\left(x+y\right)+1\)

\(\Leftrightarrow8x^3+12x^2y+6xy^2+y^3=\left(x+y+1\right)^3\)

\(\Leftrightarrow\left(2x+y\right)^3=\left(x+y+1\right)^3\)

\(\Leftrightarrow2x+y=x+y+1\)

\(\Leftrightarrow x=1\)

Với \(x=1\):

\(y\left(3+y\right)=4\)

\(\Leftrightarrow\orbr{\begin{cases}y=1\\y=-4\end{cases}}\).

Answer 2

[Đỗ Minh Châu]

y = 1

y = -4