Solving for "a" in Square Root Equation

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Homework Help Overview

The problem involves solving for the variable "a" in the equation involving square roots: \(\sqrt{6-\sqrt{a}}+\sqrt{6+\sqrt{a}}=\sqrt{14}\). The context is rooted in algebraic manipulation and understanding square root properties.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the possibility of squaring both sides of the equation as a method to simplify the problem. There are questions about the implications of squaring and whether it leads to correct interpretations of the equation.

Discussion Status

Some participants have shared their attempts at manipulating the equation, noting specific expressions they derived. There is a mix of encouragement and light-heartedness in the responses, with one participant expressing a moment of realization about their earlier confusion.

Contextual Notes

One participant mentions feeling foolish about their earlier misunderstanding, indicating a potential struggle with the algebraic concepts involved. The discussion reflects a collaborative effort to clarify the problem without providing direct solutions.

Asla
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Homework Statement


Get the value of a if
\sqrt{6-\sqrt{a}}+\sqrt{6+\sqrt{a}}=\sqrt{14}


The Attempt at a Solution


nothing succesfull
Feel free to move this thread,..I actually place it here to tap more brains
 
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square? :wink:
 
tiny-tim said:
square? :wink:
What do you mean?I square both sides?
 
square as many sides as you can find! :biggrin:
 
tiny-tim said:
square as many sides as you can find! :biggrin:
It gives me this:
12+\sqrt{36-a}=14
could I be going wrong somewhere?
 
Damn it I had never felt so foolish,..thanks I got it
 
Asla said:
It gives me this:
12+\sqrt{36-a}=14
could I be going wrong somewhere?

(a+b)² = a² + 2ab + b²

Nevermind. You've already gotten it!
 

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