Question #70499

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Answer 1 · 2017-10-20T18:12:02

$-3+4sqrt(2)$ and $4sqrt(2)$

Let $x=$ smaller number and $y=$ larger number

So according to our first sentence:

$y-3=x->color(red)(y=x+3)$

Then our second sentence says:

$6y+x^2=41$

Then plug in $y$ into our second equation:

$6(color(red)(x+3))+x^2=41$

Set this quadratic equation equal to $0$ :

$6x+18+x^2=41$

$x^2+6x-23=0$

$x=(-6+-sqrt(6^2-4(1)(-23)))/(2(1))$

$x=(-6+-sqrt(36+92))/2=-6/2+-sqrt(128)/2=-3+-sqrt(64*2)/2$

$x=-3+-(8sqrt(2))/2=-3+-4sqrt(2)$

Since our two numbers are positive numbers, $-3-4sqrt(2)$ cannot be our value for $x$ , thus:

$x=color(blue)(-3+4sqrt(2))$

Plugging that in to our first equation:

$y=color(blue)(-3+4sqrt(2))+3=4sqrt(2)$

This number is also positive, so our two numbers are:

$-3+4sqrt(2)$ and $4sqrt(2)$