Question

If P = a2 – 2bc + b2, Q = -b2 + bc – c 2 and R = c2 + cb + a2

then, find the value of P + Q + R.

Answer with proper working
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Answer 1

$\underline{\underline{\mathfrak{\Large{Solution : }}}}$



$\underline{\textsf{Given , }} \\ \\ \sf \implies P \: = \: a^2 \: - \: 2bc \: + \: b^2 \quad...(1) \\ \\ \textsf{And,} \\ \\ \sf \implies Q \: = \: -b^2 \: + \: bc \: - \: c^2 \quad...(2) \\ \\ \textsf{And,} \\ \\ \sf \implies R \: = \: c^2 \: + \: cb \: + \: a^2 \quad...(3)$




$\underline{\textsf{Add all the equations , }} \\ \\ \sf \implies P \: + \: Q \: + \: R \: = \: a^2 \: - \: 2bc \: + \: \cancel{ b^2 }\: - \: \cancel{b^2} \: + \: bc \\ \sf \qquad \qquad \qquad \quad \: \: \: \: \: \: \: - \: \cancel{c^2} \: + \: \cancel{c^2} \: + \: bc \: + \: a^2 \\ \\ \sf \implies P \: + \: Q \: + \: R \: = \: 2 {a}^{2} \: + \: \cancel{2bc} \: - \: \cancel{2bc} \\ \\ \sf \: \: \therefore \: \: P \: + \: Q \: + \: R \: = \: 2 {a}^{2}$