TS EAMCET · Maths · Application of Derivatives
If \(x\) and \(y\) are two positive integers such that \(x+y=24\) and \(x^3 y^5\) is maximum, then \(x^2+y^2=\)
- A 288
- B 296
- C 306
- D 320
Answer & Solution
Correct Answer
(C) 306
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } x+y=24 \Rightarrow y=24-x \\ & P=x^3 y^5 \Rightarrow P=x^3(24-x)^5 \\ & \frac{d P}{d x}=3 x^2(24-x)^5-5 x^3(24-x)^4=0 \\ & \Rightarrow x^2(24-x)^4[3(24-x)-5 x]=0 \\ & \Rightarrow x^3(24-x)^4(72-8 x)=0 \\ & \Rightarrow x=0,24,9 \end{aligned}\)…
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