If the curve does not intersect the curve

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

If the curve x2=−4(y−a)x^2=-4(y-a) does not intersect the curve y=⌊x2−x+1⌋y=\left\lfloor x^2-x+1\right\rfloor, where ⌊ ⌋\lfloor\ \rfloor denotes the greatest integer function, for x∈[0,1+52]x\in\left[0,\frac{1+\sqrt5}{2}\right], then (1) 13<a<1\frac13<a<1 (2) −1<a<1-1<a<1 (3) 14<a<1\frac14<a<1 (4) None of these

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