Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 8 - Section 8.3 - Solving Equations by Using Quadratic Methods - Exercise Set: 20

Answer

$x=-1$

Work Step by Step

We can write the given equation as: $(x^{1/3})^2+2x^{1/3} +1=0$ Let $u=x^{1.3}$ Then $u^2= (x^{1/3})^2$ Rewrite the given equation using the variable $u$ to obtain: $u^2+2u+1=0$ Factor the trinomial to obtain: $(u+1)(u+1)=0$ Use the Zero-Factor Property by equating each unique factor to zero. then solve: $u+1 = 0 \\u=-1$ Since $u=x^{1/3}$, then $u= -1 \\x^{1/3}=-1 \\(x^{1/3})^3=(-1)^3 \\x=-1$ Thus, the solution is $x=-1$.
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