Question

If three distinct positive numbers a,b,c are in ap such that abc=4 then value of b is always

Answer 1

Answer:

2^(2/3)

Step-by-step explanation:

Correction in question :- It should be minimum value of b should be ?

Answer :-

Let d be the common difference.

∴ b - a = c - b = d

∴ a = d + b, c = d + b ... (1)

Now , abc = 4

So from (1) we get,

(d + b) b (d + b) = 4

∴ b (b² - d²) = 4  --- (2)

Now, b² - d² < b²

So, b(b² - d²) < b³ ---- (3)

∴ b³ > 4

∴ b > 2^(2/3)

Hence minimum value is 2^(2/3).