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Source: 2015 10A #12

February 4, 2015
quadraticsalgebrapolynomialVietaquadratic formulaabsolute valueAMC

Problem Statement

Points (π,a)(\sqrt{\pi}, a) and (π,b)(\sqrt{\pi}, b) are distinct points on the graph of y2+x4=2x2y+1y^2+x^4=2x^2y+1. What is ∣a−b∣|a-b|?
<spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>π2<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>1+π<spanclass=′latex−bold′>(E)</span>1+π <span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>\dfrac{\pi}{2}\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>\sqrt{1+\pi}\qquad<span class='latex-bold'>(E) </span>1+\sqrt{\pi}
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