Question

X+1/x=√3 then x^30+x^24+x^18+x^12+x^6+1=?

Answer 1

Given:-

x+1/x=√3

To find:-

x^30+x^24+x^18+x^12+x^6+1=?

Solution:-

x+1/x=√3

(x+1/x)³=(√3)³

or, x³ +1/x³+3*x*1/x³ (x+1/x)=3√3

or,x³ +1/x³+3√3=3√3 [because we know, x+1/x=√3]

or,x³ +1/x³= 0

or, x^6+1=0

then,

x^30+x^24+x^18+x^12+x^6+1

=x^24(x^6+1) +x^12(x^6+1)+1(x^6+1)

=x^24(0) +x^12(0)+1(0)

=0

Hence, x^30+x^24+x^18+x^12+x^6+1 = 0(Ans)

Answer 2

Answer:

x+1/x=√3

(x+1/x)³=(√3)³

or, x³ +1/x³+3*x*1/x³ (x+1/x)=3√3

or,x³ +1/x³+3√3=3√3 [because we know, x+1/x=√3]

or,x³ +1/x³= 0

or, x^6+1=0

then,

x^30+x^24+x^18+x^12+x^6+1

=x^24(x^6+1) +x^12(x^6+1)+1(x^6+1)

=x^24(0) +x^12(0)+1(0)

=0

Hence, x^30+x^24+x^18+x^12+x^6+1 = 0(Ans)