Question

the product of two numbers is 36 their sum is 20 what are the numbers

Answer 1

18 + 2 = 20

18 × 2 = 36

so the numbers are 18 and 2.

hope it helps !!

Answer 2

The numbers are 2 and 18.

Given: The product of two numbers is 36 and their sum is 20.

To Find: The numbers.

Solution:

• We can solve the numerical by applying the following formulas;

            ( a - b ) = √[ ( a + b )² - 4ab ]                                                ...(1)

Where a and b are two integer values.

• If we get the equation for the sum and difference of two numbers then on solving these two equations, we can get the values of each of the numbers.

Coming to the numerical;

Let the numbers be 'a' and 'b'.

It is said that the product of two numbers is 36 and their sum is 20. So, we can write;

     a + b = 20                                                                        .....(2)

      a × b = 36                                                                        ......(3)

Now, we shall find the difference between the two numbers by putting the respective values in (1), we get;

       ( a - b ) = √[ ( a + b )² - 4ab ]    

   ⇒ ( a - b ) = √[ ( 20 )²  -  ( 4 × 36 )]

   ⇒ ( a - b ) = √( 400 - 144 )

   ⇒ ( a - b ) = √256

   ⇒ ( a - b ) =  16                                                                              ....(4)

Now, we must solve (3) and (4), to get the values of 'a' and 'b'.

Adding (3) and (4), we get;

        ( a + b ) + ( a - b ) = 20 + 16

    ⇒ 2a = 36

    ⇒  a = 18

Putting a = 18 in (4), we get;

          ( a - b ) =  16  

       ⇒ 18 - b = 16

       ⇒  b = 18 - 16

       ⇒  b = 2

Hence, the numbers are 2 and 18.

#SPJ2