find the answer then say!!!!!!!!!!!!!!!!!!!!

Geometry Level 5

The problem is based on simple trignometry identiy so please use your little mind in solving the question


The answer is 1.25.

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1 solution

Aniket Prakash
Oct 1, 2014

just use the trignometric identites the solution become more complex but don't fear latter it become easy the you got answer

Can you add more explanation?

Calvin Lin Staff - 6 years, 8 months ago

More complex, for sure. I find that y = sec ( θ ) y = \sec(\theta) is a solution to

144 y 6 168 y 5 527 y 4 + 504 y 3 + 282 y 2 336 y + 245 = 0 144y^{6} - 168y^{5} - 527y^{4} + 504y^{3} + 282y^{2} - 336y + 245 = 0 ,

which, fortunately, factors to

( 4 y 5 ) ( 36 y 5 + 3 y 4 128 y 3 3 4 2 + 28 y 49 ) = 0 (4y - 5)(36y^{5} + 3y^{4} - 128y^{3} - 34^{2} + 28y - 49) = 0 ,

which gives y = sec ( θ ) = 5 4 y = \sec(\theta) = \frac{5}{4} as a solution.

Brian Charlesworth - 6 years, 8 months ago

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Probably the last step was difficult to think.....is there any other approach to solve the problem.....using a bit calculus i could just estimate the interwal of the answer

raghav bagri - 5 years, 5 months ago

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I'm not sure what approach @Aniket Prakash had in mind that was so simple. Although this is an old problem, I do remember spending quite a bit a time trying to find a less difficult method than establishing and then factoring a degree 6 polynomial.

Brian Charlesworth - 5 years, 5 months ago

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