Giải hệ pt sau: x√y + y√x = 30 x√x + y√y = 35

Lay ptrinh duoi tru ptrinh tren ta co
Dat $a = \sqrt{x}, b = \sqrt{y}$. Khi do, he tro thanh
$$\begin{cases}
a^2 b + b^2 a = 30 (1)\\
a^3 + b^3 = 35(2)
\end{cases}$$
Lay 3.(1)+(2) ta co
$$3a^2b + 3b^2 a + a^3 + b^3 = 3.30 + 35$$
hay
$$15a^2 – 75a + 90 = 0$$
Vay $a = 2$ hoac $a = 3$. Tuong ung la $b = 3$ hoac $b = 2$.
Vay $(a,b) = (2,3)$ hoac $(a,b) = (3,2)$.
Vay (x,y) = (4,9) hoac (x,y) = (9,4).