## Find solutions to non-linear equation

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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 Quote by mackhina 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.
 Admin 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.

## Find solutions to non-linear equation

Thanks for your help Mark, that made it totally obvious. Much appreciated.

 Tags no solutions, non-linear

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