In an Arithmetic Progression, if a = 28, d = -4, n = 7, then anis:a)3b)6c)4d)7Correct answer is option 'C'. Can you explain this answer?

Question

Answer

So, the minimum value is 9

Answer

H.M of a,b,c is =3/1/a+1/b+1/c

And A.M is =a+b+c/3

Now we know for any positive numbers, A.M≥H.M

a+b+c/3≥ 3/1/a+1/b+1/c,

∴(a+b+c)(a1+b1+c1)≥9

Answer

9

Answer

9...

Answer

Given:
a, b, c are positive real numbers.

To find:
The least value of (a * b * c) * (1/a * 1/b * 1/c).

Solution:
To find the least value of the given expression, we can start by applying the AM-GM inequality.

AM-GM Inequality:
According to the AM-GM inequality, for any set of positive real numbers, the arithmetic mean (AM) of the numbers is always greater than or equal to the geometric mean (GM) of the numbers.

Mathematically, for positive real numbers a1, a2, ..., an, the inequality states:
(a1 + a2 + ... + an)/n ≥ (a1 * a2 * ... * an)^(1/n)

Applying AM-GM inequality:
Let's apply the AM-GM inequality to the given expression:
(a * b * c) * (1/a * 1/b * 1/c)

By applying the AM-GM inequality to both factors separately, we get:
(a * b * c) * (1/a * 1/b * 1/c) ≥ [(a * 1/a) * (b * 1/b) * (c * 1/c)]^(1/3)

Simplifying further, we get:
(a * b * c) * (1/a * 1/b * 1/c) ≥ (1 * 1 * 1)^(1/3)

The right-hand side of the inequality is equal to 1.

Conclusion:
From the above inequality, we can conclude that the least value of (a * b * c) * (1/a * 1/b * 1/c) is 1.

Therefore, the correct answer is option 'a' (1).

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