If x,y∈R+ satisfying x+y=3, then the maximum value of x2y is

We have 32(2x )+y≥⎝⎛(2x ) 2y⎠⎞ 1/3 ......... AM≥GM⇒(33 ) 3≥4x2y⇒x2y≤4Therefore, maximum value of x2y is 4.

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If x,y { R }^{ + } satisfying x+y=3, then the maximum value of

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If $x, y \in R^{+}$ satisfying $x + y = 3$ , then the maximum value of $x^{2} y$ is

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Camila Discussed

x, y \in R^{+}

satisfying

x + y = 3

, then the maximum value of

x^{2} y

13 mins ago

Discuss this question LIVE

13 mins ago

We have

\frac{2 ( \frac{x}{2} ) + y}{3} \geq ⎝ ⎛ (\frac{x}{2})^{2} y ⎠ ⎞^{1/3}

.........

A M \geq GM

\Rightarrow (\frac{3}{3})^{3} \geq \frac{x ^{2} y}{4}

\Rightarrow x^{2} y \leq 4

Therefore, maximum value of

x^{2} y

4

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Question Text	If $x, y \in R^{+}$ satisfying $x + y = 3$ , then the maximum value of $x^{2} y$ is
Answer Type	Text solution:1
Upvotes	150