Question

If pqr in are in the AP then find the value of p q + R cube minus 8 Cube cube

Answer 1

p³  + r³ - 8q³ = -6pqr  if pqr in are in the AP

Step-by-step explanation:

If p, q, r are in AP, then p³ + r³ – 8q³ is equal to

p q  r in AP

=> q - p = r - q

=> 2q = p + r

Cubing both sides

=> 8q³ = p³  + r³  + 3pr(p + r)

p + r = 2q

=>  8q³ = p³  + r³  + 3pr(2q)

=> 8q³ = p³  + r³  + 6pqr

=> p³  + r³ - 8q³ = -6pqr

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Answer 2

Answer:

Since p, q and r in AP

=> q - p = r - q

=> 2q = p + r

Cubing both sides

=> 8q³ = p³ + r³ + 3pr(p + r)

p + r = 2q

=> 8q³ = p³ + r³ + 3pr(2q)

=> 8q³ = p³ + r³ + 6pqr

=> p³ + r³ - 8q³ = -6pqr