Question
If p = 24 - q - r and pq + r(q +
p) = 132, then find the value of (p² + q² + r²).
Solution
We have, p = 24 - q - r So, p + q + r = 24 And, pq + r(q + p) = 132 Or, pq + qr + pr = 132 Using, (p + q + r)² = p² + q² + r² + 2(pq + qr + pr) So, 24² = (p² + q² + r²) + 2 × 132 Or, 576 = (p² + q² + r²) + 264 Or, p² + q² + r² = 576 - 264 Or, p² + q² + r² = 312
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