If the average of two numbers is 13 and the square root of their product is 12, then the difference between the numbers is:

Options:
a) 8
b) 18
c) 10
d) 12

Solution:

Let the two numbers are = a and b
Average of number = \frac{a+b}{2}=13
a+b =26
Product = \sqrt{a \times b} =12
a x b =144

Formula = (a + b)^2= a^2+b^2 + 2ab and (a - b)^2= a^2+b^2 - 2ab
(a + b)^2 - (a-b)^2= (a^2+b^2 + 2ab) - (a^2+b^2-2ab)
(a + b)^2 - (a-b)^2 = 4ab
Put the value of a+b and a x b
=> (26)^2 - (a-b)^2 = 4 \times 144
=> (a-b)^2 = 676-576 = 100 = 10^2
=> (a-b) = 10

Ans: 10

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