Question

como faturar x elevado a 6 – x elevado a 4 + 2x elevado a 2 =

Answer 1

x⁶ -x⁴+2x² =x² *(x⁴-x²+2)

x⁴-x²+2 =0

fazendo y=x²

y²-y+2=0

y'=[1+√(1-8)]/2 =(1+√-7)/2=(1+i√7)/2

y'=[1-√(1-8)]/2 =(1-√-7)/2=(1-i√7)/2

Se y=(1+i√7)/2=x² ==> x= √[(1+i√7)/2] ou x = -√[(1+i√7)/2]

Se y=(1-i√7)/2=x² ==>x= √[(1-i√7)/2] ou x = -√[(1-i√7)/2]

x⁴-x²+2 =(x-√[(1+i√7)/2])*(x+√[(1+i√7)/2])*(x-√[(1-i√7)/2] )*(x+√[(1-i√7)/2] )

x⁶ -x⁴+2x² =x² *(x-√[(1+i√7)/2])*(x+√[(1+i√7)/2])*(x-√[(1-i√7)/2] )*(x+√[(1-i√7)/2] )