已知2a-3b+c=0,3a-2b-6c=0,a,b,c均不为0,求a^3-2b^3+4c^3/a^2b-2b^2c+3ac^2

已知2a-3b+c=0,3a-2b-6c=0,a,b,c均不为0,求a^3-2b^3+4c^3/a^2b-2b^2c+3ac^2
已知2a-3b+c=0,3a-2b-6c=0,a,b,c均不为0,求a^3-2b^3+4c^3/a^2b-2b^2c+3ac^2

已知2a-3b+c=0,3a-2b-6c=0,a,b,c均不为0,求a^3-2b^3+4c^3/a^2b-2b^2c+3ac^2
2a-3b=-c
3a-2b=6c
3a-2b=6(3b-2a)=18b-12a
15a=20b
3a=4b,
2b=6c,a=3c,b=3a/4=9c/4
a^3-2b^3+4c^3
=27c^3-2*(9/4)^3c^3+4c^3
=(31-81*9/32)c^3
=(32*31-729)c^3/32
=263c^3/32
a^2b-2b^2c+3ac^2
=(9*9/4-2*81/16+9)c^3
=(81/8+9)c^3=(153/8)c^3
原式=263/(4*153)=263/612