Question

设a、b、c是实数,若a+b+c=2√a+1+4√b+1+6√c-2-14,求a(b+c)+b(c+a)+c(a+b)的

Answer 1

令a+1=x^2,b+1=y^2,c-2=z^2,则

(x^2-1)+(y^2-1)+(z^2+2)=2x+4y+6z-14

(x^2-2x+1)+(y^2-4y+4)+(z^2-6z+9)-14=-14

(x-1)^2+(y-2)^2+(z-3)^2=0

x=1,y=2,z=3

a=0,b=2^2-1=3,c=3^2+2=11

a(b+c)+b(c+a)+c(a+b)=33+33=66