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Imran ali

· started a discussion

· 1 Months ago

Ye kaisa Solution Hai (Question:99432.0)

Kuch dhang ka diya kro bhai

Question:
If x and y are both positive, then the minimum value of (x+y) \(\left ( \cfrac {1}{x}+\cfrac{1}{y} \right )\) is:
Options:
A) 0
B) 1
C) 2
D) 4
Solution:

Ans (d) x > 0 and y > 0

∴ (x + y) \(\left ( \cfrac {1}{x}+\cfrac{1}{y} \right )= 2 + \cfrac{x}{y}+\cfrac{y}{x}\)

\(= 2 +\left (k+ \cfrac {1}{k} \right ),\) where k = \(\cfrac{x}{y}\)

Since the minimum value of the expression \(\left (k+ \cfrac {1}{k} \right )\) is 2.

∴ Minimum value of the given expression is 4.

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