Determine , if , , , and…

MATHEMATICS · Subjective · AoPS · Mathematics · Multi-Variable Linear Equations · Multi-Variable Linear Equations

Problem

Determine x2+y2+z2+w2x^2+y^2+z^2+w^2, if x222−12+y222−32+z222−52+w222−72=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, x242−12+y242−32+z242−52+w242−72=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, x262−12+y262−32+z262−52+w262−72=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, and x282−12+y282−32+z282−52+w282−72=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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