College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.6 - Solving Other Types of Equations - 1.6 Exercises: 40

Answer

$x=-1$ or $x=2$

Work Step by Step

$\sqrt{3+x}=\sqrt{x^{2}+1}$ $(\sqrt{3+x})^{2}=(\sqrt{x^{2}+1})^{2}$ $3+x=x^{2}+1$ $0=x^{2}+1-x-3$ $x^{2}-x-2=0$ $(x+1)(x-2)=0$ $x+1=0$ or $x-2=0$ $x=-1$ or $x=2$ We need to confirm the solutions. First we confirm $x=-1$ Left side=$\sqrt{3+-1}=\sqrt{2}$ Right side=$\sqrt{(-1)^{2}+1}=\sqrt{1+1}=\sqrt{2}$ Which is true. Next we confirm $x=2$ Left side=$\sqrt{3+2}=\sqrt{5}$ Right side=$\sqrt{2^{2}+1}=\sqrt{5}$ Which is true.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.