Transforming Equations to Solve for Unknown Variables for Scientists

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In summary, a rough root equation is one that involves finding an approximate solution to a mathematical problem. It is useful in scientific research as it allows for quick estimations and is used in fields such as physics, engineering, and economics. However, there are limitations to using this method, such as potential errors and the inability to solve complex equations. Different methods for solving rough root equations include trial and error, estimation, and the Newton-Raphson method.
  • #1
vabamyyr
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[tex]\sqrt{x} + \sqrt{x+2} + \sqrt{x}\sqrt{x+2}=16,5-x[/tex]
 
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  • #2
Is [tex]\sqrt{x}x=x^{\frac{3}{2}}[/tex] ?
Or is this a typo?
 
  • #3
Hint:
[tex]\frac{1}{2}(\sqrt{x}+\sqrt{x+2})^{2}=x+\sqrt{x}\sqrt{x+2}+1[/tex]
 
  • #4
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
 

FAQ: Transforming Equations to Solve for Unknown Variables for Scientists

What is a rough root equation?

A rough root equation is an equation that involves finding the approximate solution to a mathematical problem. It is called "rough" because the solution is not exact, but rather an estimation that is close enough for practical purposes.

What are the different methods for solving rough root equations?

There are several methods for solving rough root equations, including trial and error, estimation, and the Newton-Raphson method. These methods involve manipulating the equation and making educated guesses to find the solution.

Why are rough root equations important in scientific research?

Rough root equations are important in scientific research because they allow scientists to quickly estimate solutions to complex problems. This can save time and resources, especially when dealing with large datasets or complicated equations.

What are some real-world applications of rough root equations?

Rough root equations are used in a variety of fields, such as physics, engineering, and economics. They can be used to estimate quantities like population growth, chemical reactions, and electrical currents.

Are there any limitations to using rough root equations?

Yes, there are some limitations to using rough root equations. They may not always provide an exact solution, and they rely on educated guesses and estimations, which can introduce errors. Additionally, some equations may be too complex to be solved using rough root methods.

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