\(p^2 - qr = 10\) .......... (1)

\(q^2 + pr = 10\) ............. (2)

\(r^2 + pq = 10\) .......... (3)

Equation (1) - (2)

\(p^2 - q^2 - r(p+q) = 0\)

\((p+q)(p-q) = r(p+q)\)

p-q = r ................. (4)

OR

p = q+r

Adding (1) (2) & (3)

\(p^2 + q^2 + r^2 = 30 + qr - pr - pq\)

\(p^2 + q^2 + r^2 = 30 + qr - p(r + q)\)

\(p^2 + q^2 + r^2 = 30 + qr - p^2\)

\(p^2 + q^2 + r^2 = 30 - (p^2 - qr)\)

Substitute value from (1)

\(p^2 + q^2 + r^2 = 30 - 10 = 20\)

Answer = 20

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