Let a, b, c, d in R^+ such that 256abcd geq ( | vedclass

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(B) Given the inequality $256abcd \geq (a+b+c+d)^4$,we can rewrite it as $(abcd)^{\frac{1}{4}} \geq \frac{a+b+c+d}{4}$.This is the Arithmetic Mean-Geo

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$8$

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(B) Given the inequality $256abcd \geq (a+b+c+d)^4$,we can rewrite it as $(abcd)^{\frac{1}{4}} \geq \frac{a+b+c+d}{4}$.This is the Arithmetic Mean-Geometric Mean ($AM$-$GM$) inequality,which holds with equality if and only if $a = b = c = d$.Given $3a + b + 2c + 5d = 11$,and substituting $a = b = c = d = k$,we get $3k + k + 2k + 5k = 11$.$11k = 11 \Rightarrow k = 1$.Thus,$a = b = c = d = 1$.Substituting these values into the expression $a^3 + b + c^2 + 5d$,we get $1^3 + 1 + 1^2 + 5(1) = 1 + 1 + 1 + 5 = 8$.

Let $a, b, c, d \in R^+$ such that $256abcd \geq (a+b+c+d)^4$ and $3a + b + 2c + 5d = 11$. Then $a^3 + b + c^2 + 5d$ is equal to:

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