If the geometric mean of two positive numbers | vedclass

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(B) Let the two positive numbers be $a$ and $b$.Given,$\sqrt{ab} = 6$ and $\frac{a+b}{2} = 6.5$.From the first equation,$ab = 36$.From the second equa

Vedclass · Accepted Answer

$4, 9$

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(B) Let the two positive numbers be $a$ and $b$.Given,$\sqrt{ab} = 6$ and $\frac{a+b}{2} = 6.5$.From the first equation,$ab = 36$.From the second equation,$a+b = 13$.We know that $(a-b)^2 = (a+b)^2 - 4ab$.Substituting the values,$(a-b)^2 = (13)^2 - 4(36) = 169 - 144 = 25$.Thus,$a-b = 5$ (assuming $a > b$).Solving the system $a+b = 13$ and $a-b = 5$:Adding the equations: $2a = 18 \implies a = 9$.Subtracting the equations: $2b = 8 \implies b = 4$.Therefore,the numbers are $4$ and $9$.

If the geometric mean of two positive numbers is $6$ and their arithmetic mean is $6.5$,then the numbers are.........

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