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


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