Find the two numbers whose A.M. is 25 and G.M. is 20. - Vidyadip

Question

Find the two numbers whose A.M. is 25 and G.M. is 20.

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Answer

Given, A.M. = 25 G.M. = 20 Now, $\text{A}.\text{M}.=\frac{\text{a}+\text{b}}{2}=25$ And, $\text{G}.\text{M}=\sqrt{\text{ab}}=20$ $\text{a}+\text{b}=50,\text{ab}=400$ $(\text{a}-\text{b})=\sqrt{(\text{a}+\text{b})^2-4\text{ab}}$ $=\sqrt{(50)^2-16000}$ $=\sqrt{2500-1600}$ $=\pm30$ $\text{a}-\text{b}=\pm30\\ {\text{a}+\text{b}=50}\\ \overline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \ \ \text{2a} = \ \ \ 80$ $\text{a}=40$ Also, $-2\text{b}=-20$ $\text{b}=10$ $\therefore$ The numbers are 40, 10.

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