Question

If x+1/x = 1 then find x^21 + x^18 + x^12 + x^9 + x^3 + 1

Answer 1

$(x + 1/x) = 1$

$We \: know \: that$

$if \: (x + 1/x) = 1$

$then \:, x³ = -1$

$means \: (x³ + 1) = 0$

$Now ,$

$(x²¹ + x¹⁸ + x¹² + x⁹ + x³ + 1)$

$=> x¹⁸(x³ + 1) + x⁹(x³ + 1) + (x³ + 1)$

$=> x¹⁸(0) + x⁹(0) + 0$

$=> 0 + 0 + 0$

$=> 0$

Answer 2

Answer:

if, x+1

=> x= -1

p(-1)= (-1)^21+(-1)^18+(-1)^12+(-1)^9+(-1)^3+1

=(-1)+(1)+(1)+(-1)+(-1)+1

=0

if, x=1

p(1)=(1)^21+(1)^18+(1)^12+(1)^9+(1)^3+1

=  1+1+1+1+1+1

=  6

Step-by-step explanation:

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