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Do positive reals exist?

Source: XIII Polish Junior MO 2018 Second Round - Problem 1

April 24, 2018
algebrasystem of equationsPythagorean TriplePoland

Problem Statement

Do positive reals a,b,c,xa, b, c, x such that a2+b2=c2a^2+ b^2 = c^2 and (a+x)2+(b+x)2=(c+x)2(a + x)^2+ (b +x)^2 = (c + x)^2 exist?
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