If k is the arithmatic mean of 2 numbers and p,q are the geometric means between the same 2 quantities . Prove that p^3 + q^3 =2kpq
Asked by pcgamingisgood
18th August 2019,
10:06 PM
Answered by Expert
Answer:
Let A and B be two given numbers.
Mean of A and B = k
→ k - A = B - k
→ 2k = A + B ... (1)
p and q are the G.M of X and Y.
p2 = Aq, q2 = pB
A = p2 /q , B = q2 /p ... (2)
Substitute the value of A and B from (2) to (1), we get
2k = (p2 /q) + (p2 /q)
→ p3 + q3 = 2kpq
Answered by Expert
19th August 2019,
3:14 PM
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