If a + 2b + 3c = 6, then the greatest value o | vedclass

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Question

Using $\mathrm{A} \mathrm{M}$. $\geq \mathrm{G.M}$

$\frac{a+2 b+\frac{3 c}{2}+\frac{3 c}{2}}{4} \geq\left(a \cdot 2 b \cdot \frac{3 c}{2} \cdot \fr

Vedclass · Accepted Answer

$\frac{9}{8}$

Vedclass · Answer

Using $\mathrm{A} \mathrm{M}$. $\geq \mathrm{G.M}$

$\frac{a+2 b+\frac{3 c}{2}+\frac{3 c}{2}}{4} \geq\left(a \cdot 2 b \cdot \frac{3 c}{2} \cdot \frac{3 c}{2}\right)^{\frac{1}{4}}$

$\Rightarrow\left(\frac{3}{2}\right)^{4} \geq \frac{9}{2} a b c^{2} \Rightarrow a b c^{2} \leq \frac{9}{8}$

If $a + 2b + 3c = 6$, then the greatest value of $abc^2$ is (where $a,b,c$ are positive real numbers)

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