Trigonometric sprint!!can u come first??

Calculus Level 3

Challenge:Do the problem within 20 seconds using your common sense. arccos x means inverse cosine of x defined within [-1,1] Consider the equation

arccos x + arccos y + arccos z = 3(pi)

Hence find the value of

9(xy + yz + zx) ???

Once done post how much time did it take you honestly. YOUR TIME STARTS NOW!!!HURRY


The answer is 27.

Incredible Mind by incredible mind , 24, India

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2 solutions

Prajwal Kavad
Dec 21, 2014

Its just opening ur eyes and seeing it carefully, by the way this problem doesnt deserve level 4 ,should be kept in level 1 or 2 ,,

Hint : arc cos can have a maximum value of pi

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Caleb Townsend
Feb 11, 2015

Took me 15 seconds!
arccos ⁡ ( x ) \arccos(x) has a maximum value of π \pi at x = − 1. x = -1. So the maximum value of the sum of three arc cosines is 3 π 3\pi at ( − 1 , − 1 , − 1 ) (-1,-1,-1) . We see that this is indeed the value given in the problem, therefore x = y = z = − 1. x = y = z = -1. Substitute these into the problem to get 9 ( 3 ) = 27 9(3) = \boxed{27}

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