A) \[\ge 2{{y}^{3}}\]
B) \[\le 2{{y}^{3}}\]
C) \[>2{{y}^{3}}\]
D) none of these
Correct Answer: C
Solution :
| \[\Rightarrow \] x, y, z are in H.P |
| \[\Rightarrow \] y = H.M. of x and z |
| \[\because \] G.M. < H.M. |
| \[\Rightarrow \] \[\sqrt{xz}>y\] |
| Again, Since A.M. > G.M. |
| (here x, y, z are unequal) |
| \[\therefore \] \[\frac{{{x}^{3}}+{{z}^{3}}}{2}>\sqrt{{{(xz)}^{3}}}>{{y}^{3}}\] |
| \[\Rightarrow \] \[{{x}^{3}}+{{z}^{3}}>2{{y}^{3}}\] |
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