If a + 2b = 6 and ab = 4, what is the value of \(\frac{2}{a} + \frac{1}{b}\) ?

A \(\frac{1}{2}\)

B 1

C \(\frac{3}{2}\)

D 2

Correct Answer: Option C

Solution:

যদি a + 2b = 6 এবং ab = 4 হয় তাহলে \(\frac{2}{a} + \frac{1}{b}\) এর মান কত ?

দেওয়া আছে, a + 2b = 6 .......... (1)

ab = 4 ...........(2)

এখন, সমীকরণ (1) কে (2) দিয়ে ভাগ করি

\(\frac{{a + 2b}}{{ab}} = \frac{6}{4}\) => \(\frac{a}{{ab}} + \frac{{2b}}{{ab}} = \frac{6}{4}\)

=> \(\frac{1}{b} + \frac{2}{a} = \frac{6}{4}\) => \(\frac{2}{a} + \frac{1}{b} = \frac{6}{4}\)

\(\frac{2}{a} + \frac{1}{b} = \frac{3}{2}\)

Shortcut: \(\frac{2}{a} + \frac{1}{b} = \frac{{a + 2b}}{{ab}} = \frac{6}{4} = \frac{3}{2}.\)