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:

JEE Main 2017 Mathematics question

If the arithmetic mean of two numbers and , , is five times their geometric mean, then is equal to:

Answer: (4)

The hypothesis is

= 5 a+b = 10.

To get , use the identity :

(a- = 100ab - 4ab = 96ab a-b = = 46 ,

taking the positive root since . Dividing the two results, the common

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Question ID VK-115827