Question 1061871
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a positive {{{highlight(cross(3_is))}}} is 3 less than a another. When 6 times the larger is added to the square of the smaller, the result is 27. 
Find the numbers.
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Let "x" be the smaller positive number.

Then the larger number is (x+3).

The condition says

{{{6(x+3) + x^2}}} = 27.

Simplify:

{{{x^2 + 6x - 9}}} = 0.

Solve the quadratic equation:

{{{x[1,2]}}} = {{{(-6 +- sqrt(36 - 4*(-9)))/2}}} = {{{(-6 +- sqrt(72))/2}}} = {{{-3 +- 3*sqrt(2)}}}.

The positive root is x = -3 + 3*sqrt(2).


<U>Answer</U>.  The smaller number is {{{-3 + 3*sqrt(2)}}}.  The larger number is {{{3*sqrt(2)}}}.
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