The geometric mean of two numbers is 6 and th | vedclass

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(B) Let the two numbers be $a$ and $b$.Given that the geometric mean is $6$,we have $\sqrt{ab} = 6$,which implies $ab = 36$.Given that the arithmetic

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$(4, 9)$

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(B) Let the two numbers be $a$ and $b$.Given that the geometric mean is $6$,we have $\sqrt{ab} = 6$,which implies $ab = 36$.Given that the arithmetic mean is $6.5$,we have $\frac{a+b}{2} = 6.5$,which implies $a+b = 13$.We can form a quadratic equation $x^2 - (a+b)x + ab = 0$ to find the numbers.Substituting the values,we get $x^2 - 13x + 36 = 0$.Factoring the quadratic equation: $x^2 - 9x - 4x + 36 = 0$.$x(x - 9) - 4(x - 9) = 0$.$(x - 4)(x - 9) = 0$.Thus,the numbers are $4$ and $9$.

The geometric mean of two numbers is $6$ and their arithmetic mean is $6.5$. The numbers are

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