Let x, y > 0. If x3y2 = 215, then the least value of 3x + 2y is
Solution
<p>x, y > 0 and x<sup>3</sup>y<sup>2</sup> = 2<sup>15</sup></p>
<p>Now, 3x + 2y = (x + x + x) + (y + y)</p>
<p>So, by A.M $\ge$ G.M inequality</p>
<p>${{3x + 2y} \over 5} \ge \root 5 \of {{x^3}\,.\,{y^2}}$</p>
<p>$\therefore$ $3x + 2y \ge 5\root 5 \of {{2^{15}}} \ge 40$</p>
<p>$\therefore$ Least value of $3x + 4y = 40$</p>
About this question
Subject: Mathematics · Chapter: Sequences and Series · Topic: Arithmetic Progression
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