w2+x2+y2+z2=?

Να υπολογισθεί η τιμή της παράστασης $w^2+x^2+y^2+z^2$, αν 

${\displaystyle \frac{x^2}{2^2-1}}+{\displaystyle \frac{y^2}{2^2-3^2}}+{\displaystyle \frac{z^2}{2^2-5^2}}+{\displaystyle \frac{w^2}{2^2-7^2}}=1$ ${\displaystyle \frac{x^2}{4^2-1}}+{\displaystyle \frac{y^2}{4^2-3^2}}+{\displaystyle \frac{z^2}{4^2-5^2}}+{\displaystyle \frac{w^2}{4^2-7^2}}=1$ ${\displaystyle \frac{x^2}{6^2-1}}+{\displaystyle \frac{y^2}{6^2-3^2}}+{\displaystyle \frac{z^2}{6^2-5^2}}+{\displaystyle \frac{w^2}{6^2-7^2}}=1$ ${\displaystyle \frac{x^2}{8^2-1}}+{\displaystyle \frac{y^2}{8^2-3^2}}+{\displaystyle \frac{z^2}{8^2-5^2}}+{\displaystyle \frac{w^2}{8^2-7^2}}=1$

1984 AIME