已知x^2+9y^2=9,x+3y=5,求xy已知2x-y=3,xy=2,求(x+1/2y)^2已知a^2-a-1=0,求a^4+1/a^4的值
问题描述：
已知x^2+9y^2=9,x+3y=5,求xy
已知2x-y=3,xy=2,求(x+1/2y)^2
已知a^2-a-1=0,求a^4+1/a^4的值
答
(1)（x+3y）^2=x^2+9y^2+6xy=25 xy=16/6=8/3
(2) x-1/2y=3/2 (x-1/2y)^2=x^2+1/4 y^2-xy =(x+1/2y)^2 -2xy=9/4
(x+1/2y)^2=9/4+2xy=9/4+4=45/4
(3)a^4+1/a^4=(a^2+1/a^2)^2 -2
a-1-1/a=0
(a-1/a)^2=a^2+1/a^2 -2=1 a^2+1/a^2=3
a^4+1/a^4=3^2-2=7
答
已知x^2+9y^2=9,x+3y=5,求xy
(x+3y)²=x²+9y²+6xy=9+6xy=25;
6xy=16;
xy=8/3;
已知2x-y=3,xy=2,求(x+1/2y)^2
(x+y/2)²
=(2x+y)²/4
=[(2x-y)²+8xy]/4
=[9+2×8]/4
=25/4;
已知a^2-a-1=0,求a^4+1/a^4的值
a-1-1/a=0;
a-1/a=1;
a²+1/a²=(a-1/a)²+2=1+2=3;
a^4+1/a^4=(a^2+1/a^2)^2-2=9-2=7;
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