A) 4
B) 5
C) 8
D) 15
Correct Answer: B
Solution :
| [b] \[\left( 2p+\frac{1}{p} \right)=4\] \[\Rightarrow \]\[2\left( p+\frac{1}{2p} \right)=4\]\[\Rightarrow \]\[\left( p+\frac{1}{2p} \right)=2\] Cubing on both sides, we get \[\left( p+\frac{1}{2p} \right)=8\] \[\Rightarrow \]\[{{p}^{3}}+\frac{1}{8{{p}^{3}}}+3p\times \frac{1}{2p}\left( p+\frac{1}{2p} \right)=8\] \[\Rightarrow \]\[{{p}^{3}}+\frac{1}{8{{p}^{3}}}+\frac{3}{2}\times 2=8\] \[\Rightarrow \]\[{{p}^{3}}+\frac{1}{8{{p}^{3}}}=8-3\]\[\Rightarrow \]\[{{p}^{3}}+\frac{1}{8{{p}^{3}}}=5\] |
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