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We have, p = 50 - q - r
So, p + q + r = 50
And, pq + r(q + p) = 816
Or, pq + qr + pr = 816
Using, (p + q + r) 2 = p2 + q2 + r2 + 2(pq + qr + pr)
So, 502 = (p2 + q2 + r2) + 2 X 816
Or, p2 + q2 + r2 = 2,500 - 1,632
So, p2 + q2 + r2 = 868
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