Question

The product of two numbers is 64. Their sum is 20. Find the numbers.

Answer 1

Let the two numbers be x and y.

Given that sum of two numbers is 20.

x + y = 20.

y = (20 - x)  ------------------- (1)



Given that product of two numbers = 64.

xy = 64  ---------- (2)



Substitute (1) in (2), we get

x * (20 - x) = 64

20x - x^2 = 64

-x^2 + 20x - 64 = 0

-1(x^2 - 20x + 64) = 0

x^2 - 20x + 64 = 0

x^2 - 16x - 4x + 64 = 0

x(x - 16) - 4(x - 16) = 0

(x - 16)(x - 4) = 0

x = 16 and x = 4.


Therefore the 2 numbers are 16 and 4.


Verification:

From (1)

x + y = 20

16 + 4 = 20.

20 = 20.


From (2)

xy = 64

16 * 4 = 64

64 = 64.


Hope this helps!

Answer 2

Hey mate..
========

Given,

The sum of the numbers is 20

Let, the numbers be x And ( 20 - x ) respectively.

Also,

The product of two numbers is 64.

So,

=> x ( 20 - x ) = 64

=> 20x - x^2 = 64

=> - x^2 + 20x - 64 = 0

=> - 1 ( x^2 - 20x + 64 ) = 0

=> x^2 - 20x + 64 = 0

=> x^2 - ( 16 + 4 )x + 64 = 0

=> x^2 - 16x - 4x + 64 = 0

=> x ( x - 16 ) - 4 ( x - 16 ) = 0

=> ( x - 4 ) ( x - 16 ) = 0

Either,

x - 4 = 0

=> x = 4

Or,

x - 16 = 0

=> x = 16

Thus,

The numbers are 4 and ( 20 - 4 ) = 16

Or,

The numbers are 16 and ( 20 - 4 ) = 4

Hope it helps !!