A Nice Math Olympiad Cubic Equation | Find all Values of X
2024 ж. 26 Сәу.
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x cube =8, X =cube root of 8... ie 2 so x=2
x^3 - 2^3 = 0 x^3 = 2^3 x = 2
X=2 2^3-8=8-8=0
How do you know, that x=2 is the only solution?
@@juergenilse3259 It is Simple. Yes it is the ONLY solution
@@ceciliafreitas7856 noTtthereis on 1 real soututttion, but there are in addition 2 complex solutions,as ou can see in thevideo or in my first commment.
@@ceciliafreitas7856 No it isn't. The degree sign says there are three solutions. One is real while two are imaginary.
Itt is easy to see, tthattt x=2 is a soluttion.So (x^3-8) is dividable by (x-2) and we get: x^3-8=(x-2)*(x^2+2x+4) So we get the 2 possibilitties x-2=0 and x^2-2x+4=0. To solve the quadratic equation, we can use pq-Formula: x=1+-sqrt(1-4) which has no real soluttions, so tthe onkk real solution for tthhis excercise is x=2. TThe 2 complex solutions are x=-1+i*sqrt(3) and --1-i*sqrt(3).