What is x in this arithmetic problem?

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    Arithmetic
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Discussion Overview

The discussion revolves around solving an arithmetic problem involving the expression x = 222,222,222,222,222,222,222^2 - 222,222,222,222,222,222,221^2. Participants explore different approaches to simplify and calculate the value of x.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem and suggests that x can be expressed as (n+1)^2 - n^2, leading to the formula x = 2n + 1, where n = 222,222,222,222,222,222,221.
  • Another participant reformulates the problem using N = 222,222,222,222,222,222, leading to a similar expression for x, although they note it is less elegant than the previous response.
  • A later reply reiterates the first approach, confirming that x = 444,444,444,444,444,444,443, while also introducing the difference of squares formula, stating that since a - b = 1, x simplifies to a + b = 444,444,444,444,444,444,443.

Areas of Agreement / Disagreement

Participants appear to agree on the final value of x, but there are variations in the methods used to arrive at that conclusion. No explicit disagreement is noted regarding the value itself.

Contextual Notes

The discussion assumes familiarity with algebraic identities and does not address potential limitations or assumptions in the methods used.

Who May Find This Useful

Readers interested in mathematical problem-solving, particularly in algebra and arithmetic operations, may find this discussion relevant.

BobG
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Easy arithmetic problem:

x=222,222,222,222,222,222,222^2-222,222,222,222,222,222,221^2

Find x.
 
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<br /> x=(n+1)^2-n^2=2n+1<br />
where n=222,222,222,222,222,222,221.
Therefore
<br /> x=444,444,444,444,444,444,443<br />
 
I set N = 222,222,222,222,222,222 so that question becomes

(n+222)^2 - (n+221)^2

after which solving for n is straightforward

Not as nice as the first response, however
 
kevinferreira said:
x=(n+1)^2-n^2=2n+1
where n=222,222,222,222,222,222,221.
Therefore
x=444,444,444,444,444,444,443

mmm...

x=a^2-b^2=(a+b)(a-b)
but a-b = 1 so
x = a+b = 444,444,444,444,444,444,443
 
Last edited:

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