已知(a+b):(b+c):(a+c)=2:3:7,求1/a:1/b:1/c
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/28 19:06:44
![已知(a+b):(b+c):(a+c)=2:3:7,求1/a:1/b:1/c](/uploads/image/z/5348509-61-9.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%88a%2Bb%EF%BC%89%3A%EF%BC%88b%2Bc%EF%BC%89%3A%EF%BC%88a%2Bc%EF%BC%89%3D2%3A3%3A7%2C%E6%B1%821%2Fa%3A1%2Fb%3A1%2Fc)
xRJ@,bIcIK6IXt>bEvQ|LIۧL&s7ݨ?*j;|d䈈Q˰*Etovo/Uez
TE=3D)HE* $}{!<>]E]RGJkPOx<'4'3TwYX(9L%&0KxF]y1V ѳ"~0b8nF.E̵mn͒IeW(-PX}n6Pa_WkkwFD{
已知(a+b):(b+c):(a+c)=2:3:7,求1/a:1/b:1/c
已知(a+b):(b+c):(a+c)=2:3:7,求1/a:1/b:1/c
已知(a+b):(b+c):(a+c)=2:3:7,求1/a:1/b:1/c
设a+b=2t (1)
b+c=3t (2)
a+c=7t (3)
三个等式相加得:
2a+2b+2c=12t
两边除以2得:a+b+c=6t (4)
(4)-(1) 得:c=4t
(4)-(2)得:a=3t
(4)-(3)得:b=-t
∴1/a:1/b:1/c
=1/(3t):1/(-t):1/(4t)
=4:(-12):3
【很高兴你解决以上问题,希望对你的学习有所帮助!】≤、≥ ∠ ²
依题意,设k
a+b=2k.....(1)
b+c=3k.....(2)
a+c=7k.....(3)
(1)+(2)+(3),得 a+b+c=6k...(4)
(4)-(1),得 c=4k
(4)-(2),得 a=3k
(4)-(3),得 b=-k
因此 原式1/a:1/b:1/c=1/3:-1:1/4=4:-12:3