Elementary Algebra

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

Chapter 9 - Roots and Radicals - Chapters 1-9 Cumulative Review Problem Set: 89

Answer

$7,9$

Work Step by Step

Consecutive odd numbers have a difference between them of $2$. If we take the smaller odd number as $x$, the larger odd number is $(x+2)$. Since the sum of the squares of the two consecutive odd numbers is 130, we write the following equation and solve: $x^{2}+(x+2)^{2}=130$ $x^{2}+x^{2}+4x+4=130$ $2x^{2}+4x+4-130=0$ $2x^{2}+4x-126=0$ $x^{2}+2x-63=0$ $x^{2}-7x+9x-63=0$ $x(x-7)+9(x-7)=0$ $(x-7)(x+9)=0$ $(x-7)=0$ or $(x+9)=0$ $x=7$ or $x=-9$ Disregarding the negative answer, we find that the smaller odd number is $7$. This means that the larger odd number is $7+2=9$.
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