Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.5 - Equations - 1.5 Exercises: 76

Answer

$x = 2 \pm \sqrt3$

Work Step by Step

$Find$ $all$ $real$ $solutions$ $of$ $the$ $quadratic$ $equation:$ $0=x^2-4x+1$ Use the Quadratic Equation Formula: $x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}$ $1x^2 -4x+1$ $a = 1, b = -4, c = 1$ $x = \frac{-(-4) \pm \sqrt {(-4)^2- 4(1 \times 1)}}{2(1)}$ $x = \frac{4 \pm \sqrt {16- 4}}{2}$ $x = \frac{4 \pm \sqrt {12}}{2}$ [Note: $\sqrt{12} = \sqrt{3\times4} = \sqrt3\times\sqrt4$ = $2\sqrt3$] $x = \frac{4 \pm 2\sqrt {3}}{2}$ $x = \frac{4}{2} \pm \frac{2\sqrt3}{2}$ $x = 2 \pm \sqrt3$
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