Question
If p = 40 - q - r and pq + r(p + q) = 400, then find the
value of (p² + q² + r²).Solution
We have, p = 40 - q - r
So, p + q + r = 40
And, pq + r(p + q) = 400
Or, pq + qr + pr = 400
Using, (p + q + r)² = p² + q² + r² + 2(pq + qr + pr)
40² = (p² + q² + r²) + 2 × 400
1600 = (p² + q² + r²) + 800
p² + q² + r² = 800
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