If $a,b,c$ are distinct positive real number and $a^{2} + b^{2} + c^{2} = 1$, then $3\left( a^{2}b^{2}c^{2} \right)^{\frac{1}{3}}$ is

Question

Dr. Abubacker · Accepted Answer

(a)
Using AM$>$GM [$	herefore a,b\ and\ c\ are\ distinct$]
$	herefore\frac{a^{2} + b^{2} + c^{2}}{3} > \left( a^{2}b^{2}c^{2} ight)^{1/3}\$
$\Rightarrow \ \ 3\left( a^{2}b^{2}c^{2} ight)^{\frac{1}{3}}\ \ \ \ \ \ \lbrack	herefore a^{2} + b^{2} + c^{2} = 1\ givenbrack$

Q. If $a,b,c$ are distinct positive real number and $a^{2} + b^{2} + c^{2} = 1$, then $3\left( a^{2}b^{2}c^{2} \right)^{\frac{1}{3}}$ is

Explanation

Reviewed by Dr. Abubacker

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