Squaring both sides of an equation?

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Discussion Overview

The discussion revolves around the mathematical process of squaring both sides of an equation, specifically in the context of simplifying an equation of the form \(\sqrt{A} + B = 0\). Participants explore the implications of squaring the equation directly versus moving terms before squaring, addressing the conditions under which these operations are valid.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question whether it is correct to square the equation as is, noting that moving terms before squaring might lead to different results.
  • One participant emphasizes the importance of considering the ranges of \(A\) and \(B\), suggesting that \(A\) must be non-negative and \(B\) should be non-positive.
  • Another participant points out that squaring the equation without transposition retains linear terms, which could complicate the simplification process.
  • It is suggested that squaring the original equation leads to a more complex expression that may not aid in simplification.
  • Some participants express confusion about the correctness of moving terms before squaring, with one asserting that it could yield a positive value incorrectly.
  • A later reply acknowledges a mistake regarding the formulation of the squared equation, indicating a need for clarity in the mathematical expression.

Areas of Agreement / Disagreement

Participants express differing views on the validity of squaring the equation directly versus moving terms first. There is no consensus on the best approach, and the discussion remains unresolved regarding the implications of each method.

Contextual Notes

Participants highlight the need to consider the ranges of \(A\) and \(B\) when discussing the squaring process, indicating that assumptions about these variables are crucial to the discussion.

bobyo
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If I wanted to simplify an equation, say of the form \sqrt{A} + B = 0 to get rid of the square root, is it correct to square as is? If so, why would it then be wrong to move one term to the other side before squaring?

Thanks
 
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Prior to beginning, you must be aware of the possible ranges of A and B.
I believe this is what you missed.
A>0 or A=0
I will assume that B is the component of the set of the entire negative real number.

If you have learned about how
(X+Y)^2 is developed,

X^2+2XY+Y^2,

you will see that the linear terms of X and Y still remain in the equation.

Now let's substitute A^(1/2) with P, and B with Q. In order to get rid of square root, every degree of P should be the multiple of 2, or 0.

P + Q = 0

If you square both sides of the equation without any transposition, that will be

P^2+2PQ+Q^2=0

and you will notice that still there is a linear term of P.

If you just want to simplify the original equation,

A=B^2 (A>0 or A=0, B<0 or B=0)

may be accurate.
 
Last edited:
What makes you think that would be wrong?
 
B must be 0 or a negative number. If he squared with one term moved to other side, he could have got a positive value.
 
Last edited:
bobyo said:
If I wanted to simplify an equation, say of the form \sqrt{A} + B = 0[/teAx] to get rid of the square root, is it correct to square as is? If so, why would it then be wrong to move one term to the other side before squaring?<br /> <br /> Thanks
<br /> <br /> It depends what you want to do. Suppose, for example, ##B = -3##, then your equation becomes:<br /> <br /> ##\sqrt{A} = -B##<br /> <br /> ##A = B^2 = 9##<br /> <br /> Whereas, squaring the original equation doesn&#039;t get you very far:<br /> <br /> ##A -6 \sqrt{A}+ 9 = 0##<br /> <br /> Which doesn&#039;t really help.
 
Haynes Kwon said:
Prior to beginning, you must be aware of the possible ranges of A and B.
I believe this is what you missed.
A>0 or A=0
I will assume that B is the component of the set of the entire negative real number.

If you have learned about how
(X+Y)^2 is developed,

X^2+2XY+Y^2,

you will see that the linear terms of X and Y still remain in the equation.

Now let''s substitute A^(1/2) with P, and B with Q. In order to get rid of square root, every degree of P should be the multiple of 2, or 0.

P + Q = 0

If you square the equation without any transposition, that will be

P^2+2PQ+Q^2
If you "square an equation" (really, square both sides of an equation), you should end up with an equation.
What you have above is missing "= 0".
Haynes Kwon said:
and you will notice that still there is a linear term of P.

If you just want to simplify the original equation,

A=B^2 (A>0 or A=0, B<0 or B=0)

may be accurate.
 
Mark44 said:
If you "square an equation" (really, square both sides of an equation), you should end up with an equation.
What you have above is missing "= 0".

Thank you. My bad.
 

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