Question

The product of two numbers is 45 and their Arithmetic mean is 7. find the numbers​

Answer 1

Xy = 45
(x+y)/2=7
---------
x+y = 14
Ah. So we can simplify the problem to, 'the product of two numbers is 45 and their sum is 14'. This shouldn't too hard to guess: the numbers are 5 and 9

Answer 2

Let the two numbers be x and y.
Now, according to question
x*y=45 (let this be eq1)and (x+y)/2=7(let this be eq2)
x+y=14
x=14-y
Putting this in eq1
(14-y)*y=45
14y-y^2=45
This is a quadratic equation
y^2-14y+45=0
You can solve a quadratic any way you want. Here factorization method is being used.
y(y-9)-5(y-9)=0
(y-5)(y-9)=0
y can be equal to 9 or 5
Using any of the y values we can find x by placing y in eq1 or 2[preferably 2 because addition]
If y=5 then x=9
If y=9 then x=5