The arithmetic mean and geometric mean of two numbers are 7 and 2√10 respectively, then find the numbers.

Correct option is C

Given:
Arithmetic mean = 7
Geometric mean = 2√10
Solution:
Let the number be a and b
As we know-
Arithmetic mean = (a+b)/2
Geometric mean = √ab
Then as per question-
​$$(a+b)/2=7\\a + b = 14 ………….(1)\\√ab=2√10\\ab = 4×10\\ab = 40…………(2)\\\text {From equation (1) on squaring both side and (2)}\\a^2 + b^2 + 2ab = 196\\a^2 + b^2 = 196 - 2ab\\a^2 + b^2 = 196 - 2×40\\a^2 + b^2 = 196 - 80\\a^2 + b^2= 116\\(a – b)^2 = a^2 + b^2 - 2ab\\(a – b)^2 = 116 - 2×40\\(a – b)^2 = 116 – 80\\(a – b)^2 = 36\\a – b = 6 ………..(3)\\\text {from equation (1) and (3)}\\a = 4 \,and \,b = 10\\$$​​