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  4. Let p =√[3]11+2 √30+√[3]11-2 √30, then the value of log 5( p 3-3 p +3) is equal to

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Q. Let $p =\sqrt[3]{11+2 \sqrt{30}}+\sqrt[3]{11-2 \sqrt{30}}$, then the value of $\log _5\left( p ^3-3 p +3\right)$ is equal to

Continuity and Differentiability

Solution:

$p ^3=11+2 \sqrt{30}+11-2 \sqrt{30}+3[(11+2 \sqrt{30})(11-2 \sqrt{30})]^{1 / 3}( P )$
$\Rightarrow p ^3=22+3 p \Rightarrow p ^3-3 p +3=25 $
$\Rightarrow\log _5(25)=2 $