Problem 32

Algebra Level 5

2 a 2 + 1 − 2 b 2 + 1 + 3 c 2 + 1 \frac{2}{a^2+1}-\frac{2}{b^2+1}+\frac{3}{c^2+1}

Given that a , b , c a,b,c be real numbers such that a b c + a + c = b abc+a+c=b .Find the maximum value of the expression above.

Give your answer to two decimal places.

Vietnam TST.
This problem is in this Set .


The answer is 3.33.

Son Nguyen by Son Nguyen , 20, Vietnam

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1 solution

Hitesh Yadav
Aug 20, 2020

Try using trigonometry , as you can see a hidden formula in the given relation. b = t a n ( B ) , c = t a n ( C ) , a = t a n ( B − C ) b=tan(B), c=tan(C), a=tan(B-C)

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