Question

The difference between two numbers is 5 and their product is 500,then the number are​

Answer 1

Let the numbers be x and y.

x-y=5 ------------1

and xy=500.----------2

Now from 1,

x=5+y.------------3.

Keeping in equation 2,

(5+y)y=500.

y^2+5y-500=0.

y^2+25y -20y-500=0.

y(y+25)-20(y+25)=0

(y-20)(y+25)=0.

Therefore y=20 or -25.

x will be 25 and -20 respectively

Answer 2

Let one number be=x

Second number is=x-5

ATQ,

x(x-5)=500

x^2-5x=500

x^2-5x-500=0

x^2+20x-25x-500=0

x(x+20)-25(x+20)=0

(x+20)(x-25)=0

x-25=0

x=25

First no.=25

Second no. 20

Thank you.