JEE MainMathematicsModerateSequences and Series

The H. M. of two positive numbers is 4. If their AM, A and GM, G
satisfy the relation 2A + G^2 = 27 then the numbers are.

Show answer and solution

H = 4,2A + G^{2} = 27

\Rightarrow 2A + AH = 27 \Rightarrow A = $\frac{a + b}{2} = \frac{9}{2} \Rightarrow a + b = 9$ $H = \frac{2ab}{a + b} = 4$ $\Rightarrow ab = 18$

\therefore a = 6,b = 3\ or\ a = 3,b = 6$$

Source: Grass-G / M-19 Mathematics Paper 28 Nov Fourth.docx

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