Question

已知2/a=3/b=5/c，且2a+b-c=4，求多项式a²-3bc-1/2c的值

已知2/a=3/b=5/c，且2a+b-c=4，求多项式a²-3bc-1/2c的值

Answer 1

设2/a=3/b=5/c=1/t，则a=2t,b=3t,c=5t
将a=2t,b=3t,c=5t代入2a+b-c=2*2t+3t-5t=2t=4,解得t=2
a=2t=2*2=4
b=3t=3*2=6
c=5t=5*2=10
将a=4,b=6,c=10代入a²-3bc-1/2c=16-180-5=-169

Answer 2

2/a=3/b=5/c=1/k
a=2k，b=3k，c=5k
2a+b-c=4，
2*2k+3k-5k=2k=4
k=2
a=2k=4,b=3k=6,c=5k=10
a^2-3bc-1/2c
=4^2-3*6*10-1/2*10
=16-180-5
=169