Question

已知实数x、y满足x^2+4xy+4y^2+x+2y-6=0,求6/(x+2y)的值

急

Answer 1

x^2+4xy+4y^2+x+2y-6=(x+2y)²+(x+2y)-6=[(x+2y)+3][(x+2y)-2]=0
得(x+2y)=-3或2
(x+2y)=-3时6/(x+2y)=-2
(x+2y)=2时6/(x+2y)=3

Answer 2

(x^2+4xy+4y^2)+(x+2y)-6=0
(x+2y)^2+(x+2y)-6=0
(x+2y+3)(x+2y-2)=0

①x+2y+3=0
x+2y=-3

6/(x+2y)=-2

②x+2y-2=0
x+2y=2

6/(x+2y)=3

Answer 3

我们设x+2y=a
原式=(x+2y)^2+x+2y-6=0
a^2+a-6=0
(a-2)(a+3)=0
a1=2 ,a=-3
6/(x+2y)=3或-2