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If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then (a + b)/(a - b) is equal to

(a)  √6/2

(b)  (3√2)/4

(c)  (5√6)/12

(d)  (7√3)/12

1 Answer

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Best answer

Correct option(c)  (5√6)/12

The arithmetic mean of two numbers a and b is

a + b/2

The geometric mean of two numbers a and b is

√ab

It is given that the arithmetic mean of two numbers a and b is five times their geometric mean. That is,

a + b/2 = 5√ab

⇒ a + b = 10ab  ....(1)

Squaring on both sides, of Eq. (1), we get

(a + b)2 = 100ab

⇒ a2 + b2 + 2ab = 100ab

⇒ a2 + b2 = 98ab

Subtracting -2ab from both sides of this equation, we get

a2 + b2 - 2ab = 98ab - 2ab

⇒ (a - b) 2 = 96ab

⇒ (a - b) = √96√ab   ......(2)

Now,

Multiplying and dividing RHS by 6, we get

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