Question

If x = $\frac{1}{√2}$( 1 + i)

Then show that,
x⁶ + x⁴ + x²+ 1 = 0


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Quality Answer✅​

Answer 1

Answer:

For any real number x :

x² ≥ 0

x⁴ = (x²)² ≥ 0

x⁶ = (x³)² ≥ 0

Hence, x⁶ + x⁴ + x² ≥ 0

and -(x⁶ + x⁴ + x²) ≤ 0

x⁶ + x⁴ + x² + x + 3 = 0

x = -(x⁶ + x⁴ + x²) - 3

Since -(x⁶ + x⁴ + x²) ≤ 0

x = -(x⁶ + x⁴ + x²) - 3 ≤ -3