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# What are three consecutive integers that equal 171?

I'm assuming this is supposed to say: "What are three consecutive integers that add together to equal 171?"

This could also be "What are three consecutive integers that multiply together to equal 171?"

I will do both.

For the addition caseThink of "three consecutive integers" as the expressions x, x+1, and x+2. For any value of x, these three expressions will give that number, the number that is one greater than it, and the number that is two greater than it. So, the expression x+(x+1)+(x+2) is the general sum of three consecutive integers. Also possible is the expression x+(x-1)+(x-2), which are still three consecutive integers.

So, this is a simple equation:

x+(x+1)+(x+2)=171

x+x+1+x+2=171

3x+3=171

3x=168

x=168/3

x=56

Since x=56, x+1=57 and x+2=58

So the three numbers are 56,57,and 58

You can check this answer by adding the three numbers together. I'll bet they equal 171.

For the multiplication case:Refer to the explanation for the addition case, but instead of the end expression being x+(x+1)+(x+2), it is now the multiplication of the three integers, meaning the expression is (x)(x+1)(x+2), so we get:

(x)(x+1)(x+2)=171

(x)(x2+3x+2)=171

x3+3x2+2x=171

I'll admit right now I don't know a simple way to solve this equation, which hints to me that addition was the intent of the question, but this equation can be solved by plotting the equations

y=x3+3x2+2x

y=171

and finding their point(s) of intersection. The value comes out to be approximately 4.6106, which means that the numbers 4.6106, 5.6106, and 6.6106 will multiply to equal approximately 171 (but not exactly). No exact answer is really possible here.

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