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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