Question #6b965

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Answer 1 · 2017-12-07T04:50:10

The two numbers are either -36 and -15
Or they are 15 and 36.

Let the smaller number be $x$ $x$ and let the larger number be $y$ $y$ .

By putting the words into equations, we get
$x y = 540$ $xy=540$
and
$y = x + 21$ $y=x+21$

Use substitution to substitute the second equation into the first:
$x (x + 21) = 540$ $x(x+21)=540$

$x^{2} + 21 x - 540 = 0$ $x^2 +21x-540=0$

Use the quadratic formula:
$x = \frac{- 21 \pm \sqrt{21^{2} - 4 (- 540)}}{2}$ $x=frac{-21 +- sqrt(21^2 - 4(-540))}{2}$

$x = \frac{- 21 \pm 51}{2}$ $x=frac{-21+-51}{2}$

$x = - 36, 15$ $x=-36, 15$

$y = - 15, 36$ $y=-15,36$