Question

the product of two numbers is 270 and their difference is 3. what will be the sum of those two numbers?​

Answer 1

Given

We have given product of two numbers is 270

and their difference is 3.

To Find

we have to find sum of those numbers

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Let us assume that the two numbers be 'x' and 'y'

according to the question:

product of two numbers is 270

then our Equation becomes: xy=270---(1)

Difference of those numbers is 3

then our Equation becomes:x-y= 3------(2)

From equation 2

we get x = 3+y -----(3)

Put X's value into equation 1

=>xy= 270

=>(3+y)y=270

=>3y+y²=270

=>y²+3y-270

It is in the form of a quadratic equation so,we use quadratic formula to find y

y= -b ± √b²-4ac / 2a

a= 1,b= 3 & c= -270

=>y= -3±√ 3²-4(1)(-270)/2

=>y= -3±√9-(-1080) / 2

=>y= -3±√9+1080 /2

=>y= -3±√1089 /2

=>y= -3±33/2

=>y = 30/2 or y= -36/2

=>y = 15 or y = -18

from equation 3

x= 3+y

=>x= 3+15 or 3+(-18)

=>x= 18 or x= -15

Sum of numbers = x+y = 18+15= 33

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$=x+y= -15+(-18)= -33