Đáp án:
`x^2+8xy^2+9 = 4y(x+3)`
`⇔ x^2+8xy^2+9 = 4xy+12y`
`⇔ (x^2-4xy+4y^2)+(4y^2-12y+9) = 0`
`⇔ (x-2y)^2+(2y-3)^2 = 0`
+Ta thấy : `(x-2y)^2≥0 ∀ x,y`
`(2y-3)^2≥0 ∀ y`
⇒ `(x-2y)^2+(2y-3)^2≥0 ∀ x,y`
⇒ \(\left[ \begin{array}{l}x+2y=0\\2y-3=0\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=-3\\y=\frac{3}{2} \end{array} \right.\)