, where a and b are two distinct numbers such that ab 0.

Question

, where a and b are two distinct numbers such that ab > 0.

Philoid · Accepted Answer

False

Given: a ≠ b and ab > 0

(Because Arithmetic Mean (AM) of a list of non- negative real numbers is greater than or equal to the Geometric mean (GM) of the same list)

⇒ AM > GM

If a and b be such numbers, then

and GM = √ab

By assuming that is true statement.

Similarly, AM and GM of a² and b² will be,

and GM = √(a².b²

So,

(By AM and GM property as mentioned earlier in the answer)

(By our assumption)

But this not possible since, -1 ≤ cos θ ≤ 1

Thus, our assumption is wrong and

, where a and b are two distinct numbers such that ab >0.