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UKMT Senior Mathematical Challenge, 2009

Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The positive numbers $x$ and $y$ satisfy the equations $x^4 - y^4 = 2009$ and $x^2 + y^2 = 49$ . What is the value of $y$ ?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) more information is needed

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