Question
If the average of two numbers is 13 and the square root
of their product is 12, then the difference between the numbers is:Solution
Sum of the numbers = 13 × 2 = 26 Let the two numbers be a and b So, (a + b) = 26 ----(i) Now, √ab = 12 ⇒ (√ab)2 = 122 ⇒ ab = 144 Now, (a + b)2 = 262 ⇒ a2 + b2 + 2ab = 676 ⇒ a2 + b2 + 2ab - 4ab = 676 - 4 × 144 ⇒ a2 + b2 - 2ab = 676 - 576 ⇒ (a - b)2 = 100 ⇒ (a - b) = 10 ----(ii) From eq (i) and eq (ii) we can say a = 18 and b = 8 Now, Difference of the two numbers = 18 - 8 ⇒ 10 ∴ The difference between the numbers is 10.
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