plz solve this problem
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( x + 1/x)² = 3
(x + 1/x) = √3
x³ + 1/x³ = ( x + 1/x)³ -3(x + 1/x) = (√3)³ -3√3
x³ + 1/x³ = 3√3 -3√3 = 0
x^6 + 1 = 0 ----------(1)
now,
x^206 + x^200 + x^90 + x^84 + x^18 + x^12 + x^6 + 1
= x^200( x^6 + 1) + x^84( x^6 +1) + x^12(x^6 + 1) + (x^6 + 1)
now put ( x^6 + 1) = 0 from eqn (1)
= x^200 × 0 + x^84 × 0 + x^12 × 0 + 0
= 0 + 0 + 0 + 0 = 0
(x + 1/x) = √3
x³ + 1/x³ = ( x + 1/x)³ -3(x + 1/x) = (√3)³ -3√3
x³ + 1/x³ = 3√3 -3√3 = 0
x^6 + 1 = 0 ----------(1)
now,
x^206 + x^200 + x^90 + x^84 + x^18 + x^12 + x^6 + 1
= x^200( x^6 + 1) + x^84( x^6 +1) + x^12(x^6 + 1) + (x^6 + 1)
now put ( x^6 + 1) = 0 from eqn (1)
= x^200 × 0 + x^84 × 0 + x^12 × 0 + 0
= 0 + 0 + 0 + 0 = 0
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