Question

Prove a^3 + b^3 > 2b^3 if a,b,c are in hp

Answer 1

Step-by-step explanation:

Given Prove a^3 + b^3 > 2b^3 if a,b,c are in hp

• So a,b,c are in h.p A.M > G.M > h.M
• Now b is harmonic mean of a and c
• So G.M of a and c will be √ac
• So √ac  >  b or (√ac)^n > b^n
• Now a^n, c^n  
• So A.M will be a^n + c^n / 2  
• G. M will be √a^n x c^n
•                 = (√ac)^n
• Now a^n + c^n / 2 > (√ac)^n  > b^n
• Therefore a^n + c^n / 2 > b^n
• Now a^n + c^n > 2 b^n
• Now n belongs to natural numbers.
• Now we have a^3 + c^3 > 2 b^3

Reference link will be

https://brainly.in/question/4645111