Solve Exponential Function: x1/2 + x-1/2 | Help & Explanation

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    Exponential Functions
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Discussion Overview

The discussion revolves around simplifying the expression (x1/2 + x-1/2)2. Participants seek clarification on the correct approach to simplify this expression, focusing on the mathematical principles involved.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant requests help in simplifying the expression and expresses confusion over their initial attempt.
  • Another participant questions the steps taken and asks for clarification on what the original poster has done so far.
  • A participant identifies errors in the original poster's computation, specifically regarding the incorrect distribution of the exponent over addition.
  • It is noted that the incorrect approach is commonly referred to as the "freshman's dream," highlighting a common misconception in mathematics.
  • A suggestion is made to use the FOIL method to correctly expand the expression.
  • The original poster later claims to have arrived at the correct answer after following the guidance provided.

Areas of Agreement / Disagreement

There is no explicit consensus on the initial approach taken by the original poster, as it is identified as incorrect. However, the later claim of having found the correct answer suggests some resolution for that participant.

Contextual Notes

Participants do not fully explore the implications of their mathematical reasoning, and there may be unresolved assumptions regarding the understanding of exponentiation and simplification techniques.

linapril
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Hello! Could someone please help me answer this question, and explain how you answered it?

1. (x1/2 + x-1/2)2​Thank you!
 
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What are you asked to do? And what steps have you made towards doing that?
 
It just says to simplify it.
I multiplied away the brackets, getting x + x, which equals 2x. But this answer's wrong apparently...
 
Yes, there are several errors in your computations. The first error, seemingly, is that you distributed the exponent over addition. This NEVER WORKS! If you don't believe me, check this out: is
$$25=5^{2}=(2+3)^{2}=2^{2}+3^{2}=4+9=13?$$
Definitely not. So this thought doesn't work. It's so common it's called the "freshman's dream". You have to write out your expression and FOIL it:
$$(x^{1/2}+x^{-1/2})^{2}=(x^{1/2}+x^{-1/2})(x^{1/2}+x^{-1/2}).$$
Now do your firsts, outers, inners, and lasts. What do you get?
 
I got the right answer, thank you so much :)
 
You're welcome! Have a good one.
 

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