If the arithmetic mean of two numbers be A and geometric mean be G, then the numbers will be

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Solution

The correct option is C

A.M. = $\frac{a + b}{2}$ = A and G.M. = $\sqrt{a b}$ = G

On solving a and b are given by the values

A $\pm \sqrt{(A + G) (A - G)}$ .

Trick : Let the numbers be 1, 9. Then A = 5 and G = 3. Now put these values in options.

Here (c) $∴ 5 \pm \sqrt{8 \times 2}$ i.e. 9 and 1

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