Question

Divide 39 into two parts such that their product is 324.

Answer 1

Let the two parts be x and y

So we have

[tex]x+y=39 xy = 324[/tex]

Combining these equations, we get a quadratic equation:

$x(39-x) = 324$

Solving:

[tex]39x-x^2=324 \newline 39x-x^2-324=324-324 \newline -x^2+39x-324=0 \newline Using \ quadratic \ formula: \newline x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \newline x=\frac{-39+\sqrt{39^2-4\left(-1\right)\left(-324\right)}}{2\left(-1\right)} \newline x = \frac{-39+\sqrt{225}}{-2} \newline x=\frac{39+15}{2} \\ or\\ x =\frac{39-15}{2}[/tex]

Now on solving this equation, we get

$x = 12, y = 27$

or

$x = 27, y = 12$

That's your answer

Answer 2

27*12 =324
And 27+12=39
It would differ with there are changes in sign