Răspuns:
Explicație pas cu pas:
3(x²+y²)-xy=5
x²+y²-5xy=-3 notam x²+y²=a si xy=b
3a-b=5 3a-b=5
a-5b=-3 -3a+15b=9 14b=14 b=1
a=5-3 a=2
x²+y²=2 (x+y)²=x²+y²+2xy=2+2=4
xy=1
x+y=2 x+1/x=2 x²-2x+1=0 x=y=1
2) x+y=3
(x+y)³=x³+y³+3xy(x+y) 27=9/2xy+3xy×3 3=(1/2+1)xy xy=2
x+2/x=3 x²-3x+2=0 x1=1 si x2=2
Doua solutii:
x=1 y=2
x=2 y=1
