A) \[xyz\]
B) \[x+y+z\]
C) \[0\]
D) \[1\]
Correct Answer: C
Solution :
Given, \[{{a}^{x}}={{b}^{y}}={{c}^{z}}=k\] (say) \[\Rightarrow \] \[a={{k}^{1/k}}\] \[b={{k}^{1/y}}\]and \[c={{k}^{1/z}}\] \[\therefore \] \[abc={{k}^{\frac{1}{x}+\frac{1}{y}+\frac{1}{z}}}\] \[\Rightarrow \] \[1={{k}^{\frac{1}{x}+\frac{1}{y}+\frac{1}{z}}}={{k}^{0}}\] (\[\because \]Given, abc = 1) On comparing, \[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0\]\[\Rightarrow \]\[xy+yz+zx=0\]
You need to login to perform this action.
You will be redirected in
3 sec
