Question

x⁴+1/x⁴+1 factorise it​

Answer 1

Answer:

[x²-(√3i-1)/2x²] [x²+(√3i+1)/2x²]

Step-by-step explanation:

= x⁴ + 1/x⁴ +1

= (x²)²+ (1/x²)²+ (x²)(1/x²)

let Y = x² and c = 1/x²

= y²+ c² + cy

using roots of a quadratic equation formula,

X = [-b±√(b²-4ac)]/2a

y = [-c ±√(c²-4(c²))]/ 2

= [-c ±√(-3c²)]/2

= (-c ±√3 c i)/2

so, equation is now = [y-(c(√3i-1)/2] [y+(c(√3i+1)/2]

= [x²-(√3i-1)/2x²] [x²+(√3i+1)/2x²]