𝒙^𝟓𝒏 + 𝒙^𝒏 + 𝟐 = ? | Olympiad Math

We first simplify the given condition. We then use algebra to add and subtract terms (algebraic balance) in order to find the final answer by factoring using the given condition.

[prabhudasmandal]

Things made easy this way. Simplified given value is x^3n--x^2n+1=0.the given expression is x^5n+x^n+2.here, xpower4n, 3n and 2n are missing. So, adjusting these missing values with +and --, we get Now clubbing these to suit the given value we get( x^5n--x^4n+x^2n) +(x^4n-x^3n+x^n) +(x^3n--x^2n+1) +1or x^2n(x^3n--x^2n+1) +x^n(x^3n--x^2n+1) +(x^3n--x^2n+1) +1.now putting the given value, we get( x^2n×0) +(x^n×0) +(0) +1=0+0+0+1=1 ans.

[frenchboy]

to make calculus easy we can put : X=x^n

[ranshen]

What role does the condition "n ∈ ℕ" play in this problem?

[BearerOfLightSonOfGod]

It's been a few days of no fap my body is twisting up and I'm watching math videos even though I don't understand them and I need to sleep. Please send help.