1-Suppose-that-a-b-and-c-are-real-numbers-such-that-a-lt-b-lt-c-and-a-3-3a-1-b-3-3b-1-c-3-3c-1-0-Then-1-a-2-b-1-b-2-c-1-c-2-

Question Number 32609 by naka3546 last updated on 01/Apr/18

1 . S u p p o s e t h a t a, b, a n d c a r e r e a l n u m b e r s s u c h t h a t a < b < c a n d a^{3} - 3 a + 1 = b^{3} - 3 b + 1 = c^{3} - 3 c + 1 = 0 .

T h e n \frac{1}{a^{2} + b} + \frac{1}{b^{2} + c} + \frac{1}{c^{2} + a} c a n b e w r i t t e n a s \frac{p}{q} f o r r e l a t i v e l y p r i m e o f p o s i t i v e i n t e g e r s p a n d q . F i n d 100 p + q