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sudha Grade:
        

If for all real values of x, 4x^2+1 divided by 64x^2-32x sin alpha+29>1/32 then alpha lies in the interval (ans 0,pi/3)

6 years ago

Answers : (1)

Puneet Mittal AskiitiansExpert-IITD
22 Points
										

Dear Sudha ,


The solution can be found by reorganizing the equation as ( 4x2 + 1 ) * 32 > 64x2 - 32xsin(alpha) + 29


or 128x2 + 32 > 64x2 - 32xsin(alpha) + 29


or 64x2 + 32xsin(alpha) + 3 > 0


The above Identity will hold true for all of x if Determinant is less than 0


because then no solution will exist such that 64x2 + 32xsin(alpha) + 3 = 0


i e D ≤ 0


or ( 32sin(alpha) )2  - 4*64*3 ≤ 0


or 32sin2(alpha) - 24 ≤ 0


or 4sin2(alpha) - 3 ≤ 0


or sin2(alpha) ≤ 3/4


this will give that alpha should lie in the Interval ( 0 , ∏/3 ) ( as sin(∏/3) = sq. root(3) / 2)


Puneet


Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.

6 years ago
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