x+y=3,xy=-2,求1/3*x²+1/3*y²a+b=3,a-b=2,求a²+b²和ab

x+y=3,xy=-2,求1/3*x²+1/3*y²a+b=3,a-b=2,求a²+b²和ab
x+y=3,xy=-2,求1/3*x²+1/3*y²
a+b=3,a-b=2,求a²+b²和ab

x+y=3,xy=-2,求1/3*x²+1/3*y²a+b=3,a-b=2,求a²+b²和ab
1、x+y=3平方得,x^2+y^2＋2xy＝9,
∴1/3*x²+1/3*y²＝（9＋4）／3＝13／3
2、a+b=3,①
a-b=2,②
①^2+②^2,得
2(a^2+b^2)=13
∴a²+b²＝13/2
①^2－②^2,得
4ab=5
∴ab＝5/4

解:x+y=3,(x+y)^2=9=x²+y²+2xy
又xy=-2, x²+y²=9-2xy=9-2*(-2)=13
1/3*x²+1/3*y²=(1/3)*(x²+y²)=13/3
解:因为a+b=3，a-b=2，
两式相加得2a=5,两式相减得2b=1
4ab=5 ab=5/4
a²+b²=(a+b)²-2ab=9-5/2=13/2