College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 1 - Equations and Inequalities - Exercise Set 1.6 - Page 178: 27


no solution

Work Step by Step

Separate the square roots on two sides. Then square both sides and combine like terms. Put all the terms on one side and factor by trial and error. Then solve for $x$ with the values found. After plugging in the possible solutions into the original equation, it is revealed that both do not work, and therefore there is no solution. $\sqrt {2x+3}+\sqrt {x-2}=2$ $\sqrt {2x+3}=2-\sqrt {x-2}$ $(\sqrt {2x+3})^2=(2-\sqrt {x-2})^2$ $2x+3=4-4\sqrt {x-2}+x-2$ $x+1=-4\sqrt {x-2}$ $(x+1)^2=(-4\sqrt {x-2})^2$ $x^2+2x+1=16(x-2)$ $x^2-14x+33=0$ $(x-11)(x-3)=0$ $x=3,11$ $\sqrt {2\times11+3}+\sqrt {11-2}\ne2$ $\sqrt {2\times3+3}+\sqrt {3-2}\ne2$ no solution
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