SOLUTION: the product of two consecuitive integers is 156. use the equation n(n=1)=156 to find the integers.

Question 159408: the product of two consecuitive integers is 156. use the equation n(n=1)=156 to find the integers.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Distribute

Subtract 156 from both sides

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for n:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=1, and c=-156

Square 1 to get 1

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

So the first number is 12 and the second number is 13 (if you only want positive integers)

Or, the first number is -13 and the second number is -12 (if you don't mind negative numbers)
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