Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.6 - Radical Equations and Problem Solving - Exercise Set - Page 729: 44



Work Step by Step

$\sqrt {2x-1}-4=-\sqrt {x-4}$ $\sqrt {2x-1}-4+4=-\sqrt {x-4}+4$ $\sqrt {2x-1}=4-\sqrt {x-4}$ $(\sqrt {2x-1})^2=(4-\sqrt {x-4})^2$ $2x-1=4*4+4*(-\sqrt {x-4})+(-\sqrt {x-4})*4+(-\sqrt {x-4})(-\sqrt {x-4})$ $2x-1=16-8\sqrt {x-4}+(\sqrt {x-4})(\sqrt {x-4})$ $2x-1=16-8\sqrt {x-4}+(x-4)$ $2x-1=16-8\sqrt {x-4}+(x-4)$ $2x-1=16-8\sqrt {x-4}+x-4$ $2x-1+4=16-8\sqrt {x-4}+x-4+4$ $2x+3=16-8\sqrt {x-4}+x$ $x+3=16-8\sqrt {x-4}$ $x-13=-8\sqrt {x-4}$ $(x-13)^2=(-8\sqrt {x-4})^2$ $x*x+x*(-13)+(-13)*x+(-13)(-13)=(-8)^2*(\sqrt{x-4})^2$ $x^2-26x+169=64*(x-4)$ $x^2-26x+169=64x-256$ $x^2-26x+169-64x+256=64x-256-64x+256$ $x^2-90x+425=0$ $(x-85)(x-5)=0$ $x-85=0$ $x=85$ $x-5=0$ $x=5$ $\sqrt {2x-1}-4=-\sqrt {x-4}$ $\sqrt {2*85-1}-4=-\sqrt {85-4}$ $\sqrt {170-1}-4=-\sqrt {81}$ $\sqrt {169}-4=-9$ $13-4=-9$ $9=-9$ (false) $\sqrt {2x-1}-4=-\sqrt {x-4}$ $\sqrt {2*5-1}-4=-\sqrt {5-4}$ $\sqrt {10-1}-4=-\sqrt {1}$ $\sqrt {9}-4=-1$ $3-4=-1$ (true)
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