AIME 1984

Algebra Level 3

Determine x2+y2+z2+w2x^2 + y^2 + z^2 + w^2 if

x22212+y22232+z22252+w22272=1\frac {x^2}{2^2 - 1^2} + \frac {y^2}{2^2 - 3^2} + \frac {z^2}{2^2 - 5^2} + \frac {w^2}{2^2 - 7^2} = 1

x24212+y24232+z24252+w24272=1\frac {x^2}{4^2 - 1^2} + \frac {y^2}{4^2 - 3^2} + \frac {z^2}{4^2 - 5^2} + \frac {w^2}{4^2 - 7^2} = 1

x26212+y26232+z26252+w26272=1\frac {x^2}{6^2 - 1^2} + \frac {y^2}{6^2 - 3^2} + \frac {z^2}{6^2 - 5^2} + \frac {w^2}{6^2 - 7^2} = 1

x28212+y28232+z28252+w28272=1\frac {x^2}{8^2 - 1^2} + \frac {y^2}{8^2 - 3^2} + \frac {z^2}{8^2 - 5^2} + \frac {w^2}{8^2 - 7^2} = 1

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