Tuesday, July 3, 2012

College Algebra, Chapter 2, 2.3, Section 2.3, Problem 56

Find all real solutions of the equation x48x2+2=0

x48x2+2=0w28w+2=0Let w=x2w28w=2Subtract 2w28w+16=2+16Complete the square: Add (82)2=16(w4)2=14Perfect Square(w4)=±14Take the square rootw=4±14Add 4w=4+14 and w=414Solve for wx2=4+14 and x2=414Substitute w=x2x=±4+14 and x=±44Take the square root


Thus, the solutions are
x=4+14,x=4+14,x=414, and x=414

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