Question

The product of 2 consecutive numbers is 1806. What are the numbers ?

Answer 1

First, let's call the two consecutive numbers:

#n# and #(n + 1)#

We can now write an equation:

#n(n + 1) = 1806#

#n^2 + n = 1806#

#n^2 + n - color(red)(1806) = 1806 - color(red)(1806)#

#n^2 + n - 1806 = 0#

We can now factor this as:

#(n + 43)(n - 42) = 0#

hope it help ##

Answer 2

Let two consecutive numbers be x and x+1.

According to question,

=) x(x+1) = 1806

=) x^2+ x = 1806

=) x^2+ x - 1806 = 0

=) x^2 + 43x - 42x - 1806 = 0

=) x(x+43) -42(x+43) = 0

=) (x-42) (x+43) = 0

Hence x = 42 and -43.

Take positive value of x = 42.

Hence two numbers are 42 and 42+1

= 42 and 43.

Hope it's helpful to u.