Question

please solve this. ......

Answer 1

 (a² + a + 1)(b² + b + a) (c² + c + 1)  

            abc

Consider a = b = c = 1

then comes 3 x 3 x 3    = 27

                         1 x 1 x 1

So minimum value comes 27

Answer 2

Given : (a^2 + a + 1)(b^2 + b + 1)(c^2 + c + 1)/abc.

Let us consider the 1st part:

⇒ (a^2 + a + 1)/a

⇒ a + (1/a) + 1.

Now,

We know that for positive real numbers, AM ≥ GM

⇒ [(x + 1/x)/2] ≥ √x * 1/x

⇒ [(x + 1/x)/2] ≥ 1

⇒ (x + 1/x) ≥ 2

⇒ a + (1/a) + 1 ≥ 3

Likewise u can solve solve the remaining parts.

The final answer will be:

⇒ (a^2 + a + 1)(b^2 + b + 1)(c^2 + c + 1)/abc ≥ 27.

Therefore, the answer is 27 - Option (3).

Hope it helps!