Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Appendix - Extra Word Problems: 35

Answer

The numbers are: $ 5 + \sqrt{3} $ and $ 5 - \sqrt3$

Work Step by Step

We call one number x and the other y. Thus, we obtain: $x+y = 10 \\ xy = 22$ Plugging in $x = 10-y$ into equation two, we obtain: $ (10-y)y=22 \\ y^2 -10y + 22 = 0 $ We apply the quadratic formula: $ x = \frac{ -b \pm \sqrt{b^2 -4ac}}{2a}$ $ x = \frac{10 \pm \sqrt{(-10)^2 -4(1)(22)}}{2}$ $ x = \frac{ 10 \pm \sqrt{12}}{2}$ $ x = 5 \pm \sqrt3$ The numbers are $ 5 + \sqrt{3} $ and $ 5 - \sqrt3$
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