Transforming Equations to Solve for Unknown Variables for Scientists

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Discussion Overview

The discussion revolves around transforming equations to solve for unknown variables, specifically focusing on a given equation involving square roots. Participants explore methods to manipulate the equation for potential solutions.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant presents the equation \(\sqrt{x} + \sqrt{x+2} + \sqrt{x}\sqrt{x+2}=16,5-x\).
  • Another participant questions whether \(\sqrt{x}x\) is equivalent to \(x^{\frac{3}{2}}\) or if it is a typo.
  • A hint is provided suggesting that \(\frac{1}{2}(\sqrt{x}+\sqrt{x+2})^{2}=x+\sqrt{x}\sqrt{x+2}+1\) could be useful for transforming the equation.
  • A later reply acknowledges the hint as key for transforming the initial equation into a square equation over a new variable.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the equation or the validity of the proposed transformations, indicating that multiple views remain on the approach to solving the problem.

Contextual Notes

There are unresolved assumptions regarding the transformation steps and the interpretation of the equation components, particularly the potential typo in the expression.

vabamyyr
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[tex]\sqrt{x} + \sqrt{x+2} + \sqrt{x}\sqrt{x+2}=16,5-x[/tex]
 
Last edited:
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Is [tex]\sqrt{x}x=x^{\frac{3}{2}}[/tex] ?
Or is this a typo?
 
Hint:
[tex]\frac{1}{2}(\sqrt{x}+\sqrt{x+2})^{2}=x+\sqrt{x}\sqrt{x+2}+1[/tex]
 
arildno said:
Hint:
[tex]\frac{1}{2}(\sqrt{x}+\sqrt{x+2})^{2}=x+\sqrt{x}\sqrt{x+2}+1[/tex]

thanks, i knew i had to transform my initial equation to square equation over new variable, so, yes, ur hint is the key, thanks again
 

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