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Let x and y be two positive real numbers such that x + y = 1, then minimum value of:-

1/x + 1/y =

(1) 2

(2) 5/2

(3) 3

(4) 4

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The correct option is (D) 4.

A.M ≥ H.M

\(\frac{x + y}{2}\) ≥ \(\frac{2xy}{x+y}\)  → \(\frac{2}{\frac{1}{x} + \frac{1}{y}}\)

\(\frac{x + y}{2}\)  ≥ \(\frac{2}{\frac{1}{x} + \frac{1}{y}}\)

= (x + y) (\({\frac{1}{x} + \frac{1}{y}}\)) ≥ 4

=  (\({\frac{1}{x} + \frac{1}{y}}\)) ≥ 4   (x + y = 1)

Minimum Value = 4.

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