2positive integers have a sum of 10 and a product of 21, what are the integers?

1 Answer
May 15, 2018

x=3 or x=7
y=7 or y=3

Explanation:

Lets say two positive integers are x and y.

So x+y = 10 and x xx y = 21

We have two equations here:
x + y = 10 ----> equation 1
xy = 21 ----> equation 2

From equation 1, make y the subject.

x + y = 10
y = 10-x --- substitute y in equation 2

xy = 21 ---- Equation 2

x(10-x) = 21 10x-x^2 = 21#

Re-arranging the equation, we get:
-x^2+10x-21=0

Lets solve for x now:

-x^2+10x-21=0

Multiply by (-1) throughout and we get:

x^2-10x+21=0

Factors are -3 and -7 as -3 + -7=10 and -3 xx (-7) = 21

x^2-10x+21=0
x^2-3x-7x+21=0
x(x-3)-7(x-3)=0
(x-7)(x-3)=0

Hence, x=7 or x=3

Substitute value of xin equation 1

Take x=7
7 + y = 10
y=10-7
y=3 -----> First value of y

Take x=3

3 + y = 10
y=10-3
y=7 ------> Second value of y

Therefore Answer is:

x=3 or x=7
y=7 or y=3

And all of them are positive.