Question

the diffrent of two number is 2 and their product is a 1 20

Answer 1

Let the smallest integer be = X
Then the larger one is = X + 2
Product of them = 120
X ( X + 2) = 120
X^2 + 2X = 120
X^2 + 2X - 120 = 0
FACTORS of 120 is
2 * 2 * 2 * 3 * 5
Now, X^2 + 12X - 10X - 120 = 0
X (X + 12) - 10 (X + 12) = 0
( X + 12) (X - 10) = 0
X = - 12 & X = 10

CASE 1.
If the number is NEGATIVE = - 12.
Therefore, the other number is - 12 + 2 = - 10

CASE 2.
If the number is POSITIVE = 10
Therefore, the other number is 10 + 2 = 12

Answer 2

Let, the numbers be x and y.
so their sum is x+y=120––––––(¡)
and their difference is x-y=2––(¡¡)
so from (¡¡) we get,
x-y=2
x=2+y–––––––––––––––––––(¡¡¡)
Now from (¡) and (¡¡¡), we get,
(2+y)+y=120
2+y+y=120
2y=120-2
y=118/2
y=59
so x=2+y=2+59=61