SOLUTION: The product of two consecutive integers is less than the square of the smaller integer. Find the larger of the two integers. The larger of the two integers is

Question 715444: The product of two consecutive integers is less than the square of the smaller integer. Find the larger of the two integers.
The larger of the two integers is
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
Call the two consecutive integers x and x+1. Their product x*(x+1) or is less than the square of the smaller. The smaller is x, its square is and

Subtract from both sides. x<0. Then the larger of the two integers x+1 < 1.

The problem has many solutions. For example if x=-1 then x+1 = 0 and the product 0*1 = 0 is less than the smaller squared = -1 squared = 1. 0 < 1.

If x=-10, then x+1 = -9. Product: 90. Smaller squared = = 100.

Let's try an x outside the solution, and as a result an x+1 outside the solution.

If x=0 then x+1 = 1. 0*1=0 and 0 squared = 0. The product is not less than the smaller number squared. That's what we expect since x+1 < 1 is the solution.

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)

RELATED QUESTIONS
The product of two consecutive integers is less than the square of the smaller integer.... (answered by unlockmath)

The product of two consecutive integers is 17 less than the square of the larger integer. (answered by lwsshak3)

The product of two consecutive integers is less than the square of the smaller integer.... (answered by Alan3354)

Find two consecutive even integers if the square of the smaller integer is 10 more than... (answered by mananth)

Find two positive even consecutive integers such that one less than the square of the... (answered by mananth)

The product of two consecutive odd integers is 10 more than the square of the smaller... (answered by stanbon,drj)

Find two consecutive integers whose product is 6 less than the square of the larger... (answered by drk)

Find two consecutive integers whose product is 6 less than the square of the larger... (answered by Ruli)

The product of two consecutive integers is 9 less than the square of the second integer,... (answered by solver91311)