Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Appendix A - Equations and Inequalities - Page 420: 47

Answer

{$\frac{1\pm2\sqrt 3}{3}$}

Work Step by Step

$(3x-1)^{2}=12$ Using generalized square root property, $3x-1=\pm\sqrt (12)$ $3x-1=\pm\sqrt (4\times3)$ $3x-1=\pm\sqrt 4\sqrt 3$ $3x-1=\pm2\sqrt 3$ Adding 1 to both sides, $3x-1+1=1\pm2\sqrt 3$ $3x=1\pm2\sqrt 3$ Dividing both sides by 3, $\frac{3x}{3}=\frac{1\pm2\sqrt 3}{3}$ $x=\frac{1\pm2\sqrt 3}{3}$ Check: $(3(\frac{1+2\sqrt 3}{3})-1)^{2}=12$ $(1+2\sqrt 3-1)^{2}=12$ $(2\sqrt 3)^{2}=12$ $4(\sqrt 3)^{2}=12$ $4(3)=12$ $12=12$ $(3(\frac{1-2\sqrt 3}{3})-1)^{2}=12$ $(1-2\sqrt 3-1)^{2}=12$ $(-2\sqrt 3)^{2}=12$ $4(\sqrt 3)^{2}=12$ $4(3)=12$ $12=12$ Therefore, the solution set is {$\frac{1\pm2\sqrt 3}{3}$}
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