Use trigonometry
Algebra
Level
3
A quadratic equation has products of roots equal to c. If the roots are of the form. (P^2 +Q^2)/(P^2+Q^2-PQ). And (P^2+Q^2)/(P^2+Q^2+PQ). Find maximum value of c P and Q are real
The answer is 1.33.
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P= asint. Q=acost. A is real Roots a^2(sin^2 t+cos^2 t)/a^2(sin^2 t+cos^2 t +sintcost)= First root=1/(1-sintcost) = 2/(2-sin2t) Second root= 2/(2+sin2t) Product of roots= 4/(4-sin^2 2t) Max value if c when sin^2 2t max which is 1 hence. Maximum value of c= 4/3 = 1.33