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Symmetric Algebraic Equation

Source: 2015 amc 10a #16

February 4, 2015

VietaalgebrapolynomialsymmetryRational Root Theoremsystem of equationsAMC

Problem Statement

y+4 = (x-2)^2, x+4 = (y-2)^2

, and

x \neq y

, what is the value of

x^2+y^2

<span class='latex-bold'>(A) </span>10\qquad<span class='latex-bold'>(B) </span>15\qquad<span class='latex-bold'>(C) </span>20\qquad<span class='latex-bold'>(D) </span>25\qquad<span class='latex-bold'>(E) </span>\text{30}