设a,b,c,x,y,z都是实数,若a^2+b^2+c^2=25,x^2+y^2+z^2=25,ax+by+cz=25,试求(2007a+5b+8c)/(2007x+5y+8z)的值

问题描述:

设a,b,c,x,y,z都是实数,若a^2+b^2+c^2=25,x^2+y^2+z^2=25,ax+by+cz=25,试求(2007a+5b+8c)/(2007x+5y+8z)的值

a^2+b^2+c^2=25,(1)
x^2+y^2+z^2=25,(2)
ax+by+cz=25,(3)
(1)+(2)-2*(3)
a^2+b^2+c^2+x^2+y^2+z^2-2ax-2by-2cz=0,
(a-x)²+(b-y)²+(c-z)²=0
a=x,b=y,c=z
(2007a+5b+8c)/(2007x+5y+8z)=1