Let x and y be two positive real numbers such that x + y = 1 . Then the minimum value of 1 x + 1 y is-

Open MARKS Web Download App

Search any question & find its solution

Question: Answered & Verified by Expert

Let

x

and

y

be two positive real numbers such that

x + y = 1

. Then the minimum value of

\frac{1}{x} + \frac{1}{y}

is-

MathematicsSequences and SeriesKVPYKVPY 2020 (SA)

Options:

A $2$
B $\frac{5}{2}$
C $3$
D $4$

Solution:

2714 Upvotes Verified Answer

The correct answer is:

4

$x + y = 1$ and $x, y > 0$

Apply $A M \geq H M$

$\frac{x + y}{2} \geq \frac{2}{\frac{1}{x} + \frac{1}{y}}$

$\Rightarrow \frac{1}{x} + \frac{1}{y} \geq 4$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.

Use on iOS or Desktop Download from Google Play