College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.4 - Radical Equations; Equations Quadratic in Form; Factorable Equations - 1.4 Assess Your Understanding - Page 118: 34

Answer

$x=25$

Work Step by Step

$\sqrt{10+3\sqrt{x}}=\sqrt x\\(\sqrt{10+3\sqrt{x}})^2=(\sqrt x)^2\\10+3\sqrt{x}=x\\10-x=-3\sqrt{x}\\(10-x)^2=(-3\sqrt{x})^2\\100+x^2-20x=9x\\x^2-29x+100=x^2-4x-25x+100=x(x-4)-25(x-4)=(x-4)(x-25)=0$ Thus $x=4$ or $x=25$ but the equation is undefined for the earlier, thus $x=25$
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