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x222−12+y222−32+z222−52+w222−72 = 1x242−12+y242−32+z242−52+w242−72 = 1x262−12+y262−32+z262−52+w262−72 = 1x282−12+y282−32+z282−52+w282−72 = 1\begin{aligned} \dfrac{x^2}{2^2-1^2}+\dfrac{y^2}{2^2-3^2}+\dfrac{z^2}{2^2-5^2}+\dfrac{w^2}{2^2-7^2} \ = \ 1 \\ \dfrac{x^2}{4^2-1^2}+\dfrac{y^2}{4^2-3^2}+\dfrac{z^2}{4^2-5^2}+\dfrac{w^2}{4^2-7^2} \ = \ 1 \\ \dfrac{x^2}{6^2-1^2}+\dfrac{y^2}{6^2-3^2}+\dfrac{z^2}{6^2-5^2}+\dfrac{w^2}{6^2-7^2} \ = \ 1 \\ \dfrac{x^2}{8^2-1^2}+\dfrac{y^2}{8^2-3^2}+\dfrac{z^2}{8^2-5^2}+\dfrac{w^2}{8^2-7^2} \ = \ 1 \\ \end{aligned}22−12x2+22−32y2+22−52z2+22−72w2 = 142−12x2+42−32y2+42−52z2+42−72w2 = 162−12x2+62−32y2+62−52z2+62−72w2 = 182−12x2+82−32y2+82−52z2+82−72w2 = 1
Determine w2+x2+y2+z2w^2+x^2+y^2+z^2w2+x2+y2+z2 if they satisfy the system of equations above.
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