A Very Nice Math Olympiad Problem | Solve for the value of x | You Need To Know This Trick | Algebra

In this video, I'll be showing you step by step on how to solve this Olympiad Maths Exponential problem using a simple trick.
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[@vincentrobinette1507]

I got X=0 and X= -4.
Case one: 0+2=2
2*2=4 4*2=8 8*2=16
Case two: -4+2= -2
-2*-2=4 4*-2= -8 -8*-2=16

[@pspprabhat]

X+2)^4=(+_2i)^4
×=(+_ 2i-2)=2(+_1-1)

[@bobbyheffley4955]

The real solutions are x=0 and x=-4. The complex solutions are x=-2+2i and x=-2-2i.

[@SpencersAcademy]

You're very much correct 👏

[@tharanathakula3588]

X = 0 is onequicksolution

[@mirkozinauer319]

(x+2)^4=16
(x+2)^4=2^4*e^(2*k*π*i)
[(x+2)^4=2^4*e^(2*k*π*i)]^(1/4)
x+2=2*e^(k*π*i/2)
x=2*e^(k*π*i/2)-2 . . . k=0, ±1, ±, 2 ±3
x=2*(cos(k*π/2)+sin(k*π/2)*i)-2
k=0; x1=2-2=0
k=1; x2=2*i-2=-2*(1-i)
k=2; x3=-2-2=-4
k=3; x4=-2*i-2=-2*(1+i)

[@SpencersAcademy]

Excellent 👌 I like your presentation.