यदि `a^(2)=by+cz,b^(2)=cz+ax,c^(2)=ax+by` हो तो `x/(a+x)+y/(b+y)+z/(c+z)` का मान क्या है ?

Options

A. 1
B. `a+b+c`
C. `1/a+1/b+1/c`
D. 0

Answer

A

Explanation

`a^(2)=by+cz`
`b^(2)=cz+ax`
`c^(2)=ax=by`
`=x/((a+x))+y/((b+y))+z/((c+z))`
`=(ax)/(a^(2)+ax)+(by)/(b^(2)+by)+(cz)/(c^(2)+cz)`
`= (ax)/(by+cz+ax)+(by)/(cz+ax+by)+`
`(cz)/(ax+by+cz)=(ax+by+cz)/(by+cz+ax)=1`.