Question

arithmetic mean and product of two numbers are 7 and 45 respectively .find the numbers.

Answer 1

Let those  numbers  be  x and  y

Now,

We know that , arithmetic mean  of of two numbers a and  b is  given by  (a+b)/2

Arithmetic  mean of  x and  y = 7

(x+y)/2 = 7

x + y = 14

y = 14 - x .......i)

Again,

product  of  numbers = 45

 xy = 45

Putting  y = 14 -x,

x(14 - x) = 45

14x - x² = 45

x² - 14x + 45 = 0

x² - 9x - 5x + 45 = 0

x(x - 9) - 5(x - 9) = 0

(x - 5)(x - 9) = 0

x = 5 or  x = 9

When x = 5, y = 9

          x = 9 , x = 5

Hence, Numbers  are  5  and 9