find the value of a 3 + b 3 + c 3 a^3+b^3+c^3 where a , b , c a,b,c are the roots of x 3 − 2018 x + 1 x^{3} - 2018x +1

Level 2

Find the value of a 3 + b 3 + c 3 a^{3}+b^{3}+c^{3} where a , b , c a,b,c are the roots of x 3 − 2018 x + 1 x^{3} - 2018x +1 .


The answer is -3.

Bulbuul Dev by Bulbuul Dev , 37, India

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1 solution

X X
Apr 19, 2018

Because a + b + c = 0 , a b + b c + c a = − 2018 , a b c = − 1 a+b+c=0,ab+bc+ca=-2018,abc=-1 , a 3 + b 3 + c 3 = ( a + b + c ) 3 − 3 ( a + b + c ) ( a b + b c + c a ) + 3 a b c = − 3 a^3+b^3+c^3=(a+b+c)^{3}-3(a+b+c)(ab+bc+ca)+3abc=-3

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