Question 1045026
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The product of two positive numbers is.     5/6 and their quotient is 15/8. Calculate the numbers.
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<pre>
Let "x" and y" be the two numbers.

We have

xy = {{{5/6}}},       (1)   and
{{{x/y}}} = {{{15/8}}}.      (2)

Multiply (1) and (2) (both sdes). You will get

{{{x^2}}} = {{{(5*15)/(6*8)}}} = {{{25/16}}}.

Hence,  x = +/- {{{5/4}}}.

Next, divide (1) by (2) (both sides). You will get

{{{y^2}}} = {{{5/6}}} : {{{15/8}}} = {{{(5*8)/(6*15)}}} = {{{4/9}}}.

Hence, y = +/- {{{2/3}}}.

<U>Answer</U>. There are two solutions: (x,y) = ({{{5/4}}},{{{2/3}}})  and  (x,y) = ({{{-5/4}}},{{{-2/3}}}).

        // We should exclude the second solution, since the numbers are negative. 
</pre>