120/(V1-V2) + 120/(V1+V2) = 288/V2怎么解出来的????

来源:百度知道 编辑:UC知道 时间:2024/05/02 02:39:31
120/(V1-V2) + 120/(V1+V2) = 288/V2怎么解出来的???? 答案我知道是3/2......

120/(V1-V2) + 120/(V1+V2) = 288/V2
120(2*V1)/(V1+V2)(V1-V2)=288/V2
V1*V2/(V1+V2)(V1-V2)=288/240=6/5
即(V1+V2)(V1-V2)/V1*V2
=(V1/V2)-(V2/V1)=5/6
令V1/V2=a,(a>1/a,因为(V1/V2)-(V2/V1)=5/6>0),得:
a-1/a=5/6
6a^2-5a-6=0,(a不等于0且a>1/a)
(2a-3)(3a+2)=0,a=2/3或a=-3/2(舍去),
所以a=2/3,1/a=3/2
即V1/V2=2/3,V2/V1=3/2.