Inequality..very nice..

Given are three real numbers a,b,c. satisfying abc+a+c=b.

Prove that 2a²+1 - 2b²+1 + 3c²+1â‰¤103. Can the equality hold?

PS. This does not require any inequality theorem(not even Am-Gm). I cant claim to have solved this 100% by myself.:(

2 Answers

hint: try a trig substitution.:)

abc+ a+c = b

a+c = b(1-ac)

b = a+c1-ac

try a trig sub

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