यदि `(xy)/(x+y)=a,(xz)/(x+z)=b` और `(yz)/(y+z)=c` है जहां `a,b,c` सभी अशून्य संख्याऐं है तो `x` का मान किसके बराबर है?

Options

A. `(2abc)/(ab+bc-ac)`
B. `(2abc)/(ab+ac-bc)`
C. `(2abc)/(ac+bc-ab)`
D. `(2abc)/(ab+bc-ac)`

Answer

C

Explanation

`(xy)/(x+y)=a, (xz)/(x+z)=b, (yz)/(y+z)=c`
Now
`implies (x+y)/(xy)=1/a`
`(x+z)/(xz)=1/b,(y+z)/(yz)=1/c`
`implies 1/y+1/x=1/a,1/z+1/x=1/b`,
`1/z+1/y=1/c`
Now we have to findthe value of `x`
`:. 1/a+1/b-1/c=1/y+1/x+1/z`
`+1/x-1/y-1/z`
`:. 1/a+1/b=1/c=2/x`
`(bc+ac-ab)/(abc)=2/x`
`x=(2abc)/(bc+ac-ab)`