Question

Given the cubic trinomial equation x^3+2x^2+2x+1=0 , find the value of x^{1994}+x^{1997}+x^{2000}

Collected in the board: Algebraic equation

Steven Zheng Steven Zheng posted 1 week ago


Answer

Factoring the cubic polynomial to solve the function.

x^3+2x^2+2x+1=0

(x^3+x^2)+(x^2+2x+1)=0

x^2(x+1)+(x+1)^2=0

(x+1)(x^2+x+1)=0

(x+1)(x^2+x+\dfrac{1}{4}+\dfrac{3}{4} )=0

(x+1)\Big[ (x+\dfrac{1}{2})^2+\dfrac{3}{4}\Big] =0

\therefore x=-1

x^{1994}+x^{1997}+x^{2000}

=1

Steven Zheng Steven Zheng posted 1 week ago

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