It Blinds Me!

Algebra Level 5

Determine w2+x2+y2+z2w^2+x^2+y^2+z^2 if

x2221+y22232+z22252+w22272=1\dfrac{x^2}{2^2-1}+\dfrac{y^2}{2^2-3^2}+\dfrac{z^2}{2^2-5^2}+\dfrac{w^2}{2^2-7^2}=1

x2421+y24232+z24252+w24272=1\dfrac{x^2}{4^2-1}+\dfrac{y^2}{4^2-3^2}+\dfrac{z^2}{4^2-5^2}+\dfrac{w^2}{4^2-7^2}=1

x2621+y26232+z26252+w26272=1\dfrac{x^2}{6^2-1}+\dfrac{y^2}{6^2-3^2}+\dfrac{z^2}{6^2-5^2}+\dfrac{w^2}{6^2-7^2}=1

x2821+y28232+z28252+w28272=1\dfrac{x^2}{8^2-1}+\dfrac{y^2}{8^2-3^2}+\dfrac{z^2}{8^2-5^2}+\dfrac{w^2}{8^2-7^2}=1

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