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If p+q=r then p³+q³+3pqr=? |
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Answer» Answer: P^3+Q^3+R^3=0P 3 +Q 3 +R 3 =0 Step-by-step explanation: It is given that P+Q+R=0 We have to prove that : P^3+Q^3+R^3=0P 3 +Q 3 +R 3 =0 We KNOW that P^3+Q^3+R^3-3PQR=(P+Q+R)(P^2+Q^2+R^2-PQ-QR-PR)P 3 +Q 3 +R 3 −3PQR=(P+Q+R)(P 2 +Q 2 +R 2 −PQ−QR−PR) P^3+Q^3+R^3-3PQR=0\times (P^2+Q^2+R^2-PQ-QR-PR)P 3 +Q 3 +R 3 −3PQR=0×(P 2 +Q 2 +R 2 −PQ−QR−PR) P^3+Q^3+R^3-3PQR=0P 3 +Q 3 +R 3 −3PQR=0 P^3+Q^3+R^3=3PQRP 3 +Q 3 +R 3 =3PQR Hence PROVED. |
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