Find solutions to non-linear equation

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Homework Help Overview

The discussion revolves around the non-linear equation (t-1)^4 + 5 = 3, with participants seeking to understand the reasoning behind the assertion that there are no solutions. The subject area pertains to algebra and the properties of even powers in equations.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of the equation being equivalent to (t - 1)^4 = -2, questioning the existence of real solutions for even powers. There is an emphasis on understanding the intuition behind the lack of solutions rather than simply accepting the conclusion.

Discussion Status

The discussion is active, with participants providing insights into the nature of the equation and its implications. Some guidance has been offered regarding the properties of even powers, and there is acknowledgment of the need for clarity in understanding the problem.

Contextual Notes

There is a note that while there are no solutions in the set of real numbers, this does not imply that solutions do not exist in other contexts. Participants are encouraged to consider the broader implications of the equation.

mackhina
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Question:

(t-1)^4+5=3

I know the answer to the question states that there are no solution, but I would like to understand the intuition behind this. If I had this in a test I would waste ages trying to work out why I couldn't solve it.

Any advice would be heaps appreciated.

Thanks

Mick
 
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mackhina said:
Question:

(t-1)^4+5=3

I know the answer to the question states that there are no solution, but I would like to understand the intuition behind this. If I had this in a test I would waste ages trying to work out why I couldn't solve it.
This equation is equivalent to (same solution set) (t - 1)4 = -2. There are no real numbers that can be raised to the fourth power to result in a negative number, so the solution set is empty.

The same would be true if (t - 1) were raised to any even power.
 
Start solving, you should find out what the reason is quite fast.

Please use the template next time.

Note: there is no solution in R (real numbers), it doesn't mean there is no solution at all.

Edit: beaten by Mark.
 
Thanks for your help Mark, that made it totally obvious. Much appreciated.
 

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