Question

If A be the A.M. of two positive unequal quantities x and y and G be their G. M, then
fa) A<G
(b) A>G
(c) AZG
(d) ASG​

Answer 1

Concept-

Use the formula of AM = (x + y)/2 and GM = √x y.

Given-

A be the A.M. of two unequal quantities x and y and G be their G. M.

Find-

Choose the correct option-

(a) A < G

(b) A > G

(c) A ≥ G

(d) A ≤ G​

Solution-

A is the A.M. of x and y.

According to the question,

(x + y)/2 = A  → Equation (1)

G is the G.M. of x and y.

According to the question,

√ab = G  → Equation (2)

Now, (a + b)² > 0

or, (a + b)² - 4ab > 0

or, (a + b)² > 4ab

or, (a + b)² / 4 > ab

or, (a + b) / 2 > √ab     [ By squaring both sides.]

or, A > G

Therefore, correct option is (b) , i.e. , A > G.

#SPJ1