Question

$x^{2}$/у+у2/х=18,
х+у=12

Answer 1

x+y=12   y=12-x
x²/y+y²/x=18  
(x³+y³)/xy=18 
(x+y)(x²-xy+y²)=18xy
12*(x²+2xy-3xy+y²)=18xy   |÷6
2((x²+2xy+y²)-3xy)=3xy
2((x+y)²-3xy)=3xy
2(12²-3xy)=3xy
288-6xy=3xy
9xy=288
xy=32     
x(12-x)=32
12x-x²=32
x²-12x+32=0   D=16
x₁=4    y₁=8
x₂=8    y₂=4.