已知4a-3b-6c=0,a+2b-7c=0,求(2a^2+3b^2+6c^2)/(a^2+5a^2+7c^2)的值.

4a-3b-6c=0 (1)
a+2b-7c=0(2)
(1)*2+(2)*3
8a-6b-12c+3a+6b-21c=0
11a-33c=0
a=3c
(1)-4*(2)
4a-3b-6c-4a-8b+28c=0
-11b+22c=0
b=2c
所以(2a^2+3b^2+6c^2)/(a^2+5b^2+7c^2)
=(2*9c^2+3*4c^2+6c^2)/(9c^2+5*4c^2+7c^2)
=36c^2/36c^2
=1