Mathegoras

Trigonometry › Trigonometric equations › Counting solutions

Roots in [0,1] after sine substitution

High school · ●●●●○ 100 pts

Using a suitable substitution, determine the number of roots of the equation 8x(1−2x2)(8x4−8x2+1)=18x(1-2x^2)(8x^4-8x^2+1)=1 that lie in the interval [0,1][0,1].

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trigonometric substitutioncounting roots