A) \[\frac{x}{y}\]
B) \[\frac{y}{z}\]
C) \[\frac{z}{R}\]
D) \[\frac{R}{x}\]
Correct Answer: D
Solution :
Let\[\frac{x}{y}=\frac{y}{z}=\frac{z}{R}=k,\] Then,\[x=yz,\,\,y=kz,\,\,z=kR\] Also,\[\frac{x}{y}\times \frac{y}{z}\times \frac{z}{R}={{k}^{3}}\] \[\Rightarrow \] \[{{k}^{3}}=\frac{x}{R}.\] \[\therefore \]\[\frac{{{y}^{3}}+{{z}^{3}}+{{R}^{3}}}{{{x}^{3}}+{{y}^{3}}+{{z}^{3}}}\] \[=\frac{{{y}^{3}}+{{z}^{3}}+{{R}^{3}}}{{{(yz)}^{3}}+{{(kz)}^{3}}+{{(kR)}^{3}}}=\frac{{{y}^{3}}+{{z}^{3}}+{{R}^{3}}}{{{k}^{3}}({{y}^{3}}+{{z}^{3}}+{{R}^{3}})}\] \[=\frac{1}{{{k}^{3}}}=\frac{R}{x}.\]
You need to login to perform this action.
You will be redirected in
3 sec
