Radicals equations-negative square root and two radicals

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Homework Help Overview

The discussion revolves around radical equations, specifically addressing the implications of negative square roots and the existence of real solutions. Participants are examining the conditions under which certain radical expressions are defined and solvable.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions the validity of solutions involving negative square roots and whether real solutions exist for the given equations. Some participants explore the implications of variable conditions, such as the sign of y, on the definition of square roots.

Discussion Status

Participants are actively engaging with the problem, with some suggesting that certain expressions have no real solutions. There is acknowledgment of useful tools like WolframAlpha for checking solutions, indicating a collaborative exploration of the topic.

Contextual Notes

There is a focus on the conditions under which the square root functions are defined, particularly regarding negative values of y and the implications for real solutions. The discussion reflects uncertainty about the nature of the solutions based on these conditions.

Coco12
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Is the answer to sqrt -81y^3 : y sqrt-81y? or is there no real solutions?

Also for this radical equation:
sqrt 2n-5 - sqrt 3n+4=2
I worked it out and can't seem to get an answer. Is there no real solutions?
 
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if y<0, then ##\sqrt{-81y^3}=|y|\sqrt{-81y}##, otherwise the square root is not defined in the real numbers.

Your equation has no real solutions. You can check this with WolframAlpha, for example.
 
thank you so much, that WolframAlpha thing is very useful!
 
That \sqrt{-81 y} can be further simplified by noting that 92 = 81 and -y = |y| , for y smaller or equal to 0.
 

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