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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2022 · Mathematics · Basics of Mathematics

If x y=4225 where x, y are natural numbers, then what is the...

If xy=4225x y=4225 where x,yx, y are natural numbers, then what is the minimum value of x+yx+y ?

Options

  1. A130
  2. B260
  3. C2113
  4. D4226

Correct answer

A. 130

Step-by-step solution

xy=4225⇒y=4225xx y=4225 \Rightarrow y=\frac{4225}{x} Let S=x+y=x+4225xdsdx=1−4225x2=0⇒x=65S=x+y=x+\frac{4225}{x}\frac{\mathrm{ds}}{\mathrm{dx}}=1-\frac{4225}{\mathrm{x}^2}=0\Rightarrow x=65d2sdx2=2.4225x3(d2sdx2)(x=65)=2.4225(65)3>0\begin{aligned} & \frac{\mathrm{d}^2 \mathrm{ s}}{\mathrm{dx}^2}=\frac{2.4225}{\mathrm{x}^3} \\ & \left(\frac{\mathrm{ d}^2 \mathrm{ s}}{\mathrm{dx}^2}\right)_{(\mathrm{x}=65)}=\frac{2.4225}{(65)^3} > 0\end{aligned}∴x+y\therefore \quad x+y is minimum at x=65 and y=65∴y=65\therefore \quad Minimum value of x+y=65+65=130x+y=65+65=130
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