Question

If x + 1/x = root 3, find the value of x^30 + x^24 + x^18 + x^12 + x^6 + 1​

Answer 1

Answer:

x+1x=3–√

(x+1x)3=(3–√)3

x3+1x3+3.x.1x.(x+1x)=33–√

x3+1x3+33–√=33–√

x3+1x3=0

x3=−1x3=>x6=−1

squaring, x12=1

(x6)3=(−1)3=>x18=−1

x18+x12+x6+1=−1+1−1+1=0