Find solutions to non-linear equation

[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.

Any advice would be heaps appreciated.

Thanks

Mick

 

[Mark44]

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.

 

[Borek]

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.

 

[mackhina]

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