Question

The product of two consecutive integers is 240. Find the consecutive integer.

Answer 1

Answer:

Let,

The first consecutive integer is  x  

So the second consecutive integer is  (x+1)  

According to the question,

x(x+1)=240  

or,  x²+x=240  

or,  x²+x−240=0  

or,  x²+16x−15x−240=0  

or,  x(x+16)−15(x+16)=0  

or,  (x+16)(x−15)=0  

So, either  x+16=0  

hence,  x=−16  

Or,

x−15=0  

so,  x=15  

Now, if x=−16  

The first consecutive integer is  −16  

So the second consecutive integer is (−16+1)=−15  

Again, if  x=15  

The first consecutive integer is  15  

So the second consecutive integer is  (15+1)=16  

So, the consecutive integers are  −16 , −15 , or  15 , 16