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If R>0, and c,d and e are each different negative integers, what is the smalest that c could be?

You are assuming that R is an interger >0. But in the problem c,d,e are defined as negative intergers. R may not be an integer - isn't it?

If we take, R=2√3; c=-12, d=-7, e=-5 then, c+d+e=-24

so, R^(c+d+e) = (2√3)^-24 = 12^-12 That's why I think answer is A. Feedback pls.

But how can you 'guess'tify R to be a non-integer
Even if c+d+e = -24 , why C is -12 , why can't it be -22 ?
Per the question C, D and E need to be -negetive integers , So each one of them may atmost be -1.

So this gives us C to be -22 ?
I feel (A) should be - 22 (may be a typo ). _________________