If the average of two numbers is 13 and the square root

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.