MathLabs

Problem 3

Let a,b,ca,b,c be real numbers. Consider acos⁡2x+bcos⁡x+c=0a\cos^2x+b\cos x+c=0. Using a,b,ca,b,c, form a quadratic equation in cos⁡2x\cos2x whose roots are the same values of xx. Compare the equations for a=4a=4, b=2b=2, c=−1c=-1.
Step 1 of 4: Isolate the odd-power term
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acos⁡2x+c=−bcos⁡xa\cos^2x+c=-b\cos x
Detailed analysis

Rewrite the original equation as acos⁡2x+c=−bcos⁡xa\cos^2x+c=-b\cos x. Squaring will eliminate the odd power of cos⁡x\cos x.