Question

The product of two numbers is 36 and their sum is 37. What is their difference?

Answer 1

Hello,
Let's be a the greatest number, b the smallest

Method 1:

a+b=37 ==>b=37-a
a*b=36==>a(37-a)=36
==> a²-37a+36=0
==>a²-36a-a+36=0
==>a(a-36)-(a-36)=0
==>(a-36)(a-1)=0
(a=36 and b=37-36=1) or (a=1 and b=37-1=36) but a>b ==>exclude
==>a-b=35

Method 2:

a*b=36
a+b=37 ==>(a+b)²=37²
(a+b)²-4ab=37²-4*36
==>a²+2ab+b²-4ab=1225
==>(a-b)²=35²
==>a-b=35 or a-b=-35 (to exclude since a>b)

Answer 2

Let the numbers be a and b;
ab=36-------------(i)
a+b=37-----------(ii)
Make a the subject in equation II;
a=37-b
Replacing the new value of a in equation (i)
(37-b)b=36
37b-$b^{2}$=36
$b^{2} -37b+36=0$
$b^{2} -b-36b+36=0$
b(b-1)-36(b-1)=0
(b-36)(b-1)=0
b=36 0r b=1
So the numbers are 36 and 1;
Their difference 36-1=35