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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