IIT JEE , AIEEE Forum - Mathematics , Algebra

konichiwa2x

This doesn't look good at all to me. The cubic equation

has only one real root, namely

. It has a pair of complex roots

. Notice that

is large (roughly

), while

and

are small (roughly

).

In the expression

, the two terms in

will tend to swamp the others. But

is real, and

has a substantial non-real component, since

. But i dont see how the expression could possibly be a real integer.