A) (a)\[118\frac{1}{2}\]
B) \[30\frac{10}{27}\]
C) \[0\]
D) \[1\]
Correct Answer: B
Solution :
| [b] \[3x+\frac{1}{2x}=5\] \[\Rightarrow \] \[\frac{3}{2}\left( 2x+\frac{1}{3x} \right)=5\] \[\Rightarrow \] \[2x+\frac{1}{3x}=\frac{10}{3}\] (i) \[\Rightarrow \] \[{{\left( 2x+\frac{1}{3x} \right)}^{3}}=\frac{1000}{27}\] \[\Rightarrow \] \[8{{x}^{3}}+\frac{1}{27{{x}^{3}}}+3\times 2x\times \frac{1}{3x}\left( 2x\frac{1}{3x} \right)\] \[=\frac{1000}{27}\] \[\Rightarrow \] \[8{{x}^{3}}+\frac{1}{27{{x}^{3}}}+2\times \left( \frac{10}{3} \right)=\frac{1000}{27}\] [from Eq. (i)] \[\Rightarrow \]\[8{{x}^{3}}+\frac{1}{27{{x}^{3}}}=\frac{1000}{27}-\frac{20}{3}=\frac{820}{27}=30\frac{10}{27}\] |
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