U.S.A Math Olympiad - Trap Question | Can you solve?

Maths Olympiads are held all around the world to recognise students who excel in maths. The test is offered at many grade levels and provides them with numerous possibilities to win certifications, awards, and even scholarships for higher studies.

[a_voice_in_the_wilderness]

Why can't we infer that x = i^4 ? The square root of i^4 is i^2 which is, as we know: -1.

[Jabez]

This problem demonstrates that math can be inconsistent and frustrating.

[HailAnts]

Since when does the √ symbol mean _positive_ square root?! It just means square root.

If you graph y=√x you get a sideways parabola, not half a sideways parabola..

[mathisnotforthefaintofheart]

I was thinking Complex too, but then it was x instead of z...

[alihoussney]

The square root of 1 IS plus OR MINUS 1 since every positive number has two square roots. But in this problem there is no solution because the left side is asking for the positive square root.

[Vazidkhan]

We can have solution in complex number system

[thenetsurferboy]

Try it this way. Do not square. Take the square root of both sides. Then x to power 1/4 = root -1
Then x to power 1/4 = i by definition in complex numbers
From here I am sure there is a solution.

[joserafeldominguezrodrigue]

Me gusta tu manera de resolver los problemas algebraicos, pero me gustaría que cuando terminas el problema y muestras tu resultado, también muestres la ecuación que resolviste, a lo que voy, gracias…❤😊

[boristhethoughtdodger]

I understand this problem thus: "find all Xs such that each of them has "-1" among its square roots". Through complex numbers roots we see that x=1 is one and the only such number. To claim a "trick" here is a pure professorial sadism.

[DominickAngelo]

You mean that it is a “trick” question, not a trap question. Leave it to the USA to use a question like this. Can you give more logarithmic questions please?

[DominickAngelo]

You mean that it is a “trick” question, not a trap question. Leave it to the USA to use a question like this.

[rachiddahmich]

On à : i^2= -1
Alors : × = i^4 dans l'ensemble c

[ulisses_nicolau_barros]

No solution in the Real. In the Complexs there are solutions. I saw this on bprp channel or Dr Peyan's.

[muslim]

why people need to make traps?
Be simple