Question

A product of two consecutive is 56. find the integers

Answer 1

Two consecutive integers are of the form

x and x + 1

Their product is equal to 56

x(x + 1) = 56

Solve and find the two numbers x and x + 1. The above equation may be written as follows

x2 + x - 56 = 0

Factor and solve

(x - 7)(x + 8) = 0

solutions: x = 7 , x = -8

x= - 8 is not valid since the number sought must be positive. Hence

x = 7 and x + 1 = 8 are the two consecutive numbers.

Answer 2

let first integer=x
then 2nd integer will be=x+1
acc. to question
x(x+1)=56
x^2+x=56
x^2+x-56=0
x^2+8x-7x-56=0
x(x+8)-7(x+8)=0
(x+8)(x-7)=0
x+8=0 or x-7=0
x=-8 or x=7
first +ve integer=7
2nd +ve integer=7+1=8


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