Question

Solve x⁴ - x² + 1 = 0. Give your answers in the form a + ib, where a, b∈R. urgent please help​

Answer 1

`\displaystyle\\ Answer:\ x=б\sqrt{(1)/(2)-i(√(3) )/(2) } \ \ \ \ x=б\sqrt{ (1)/(2) +i(√(3) )/(2) }`

Explanation:

`\displaystyle\\x^4-x^2+1=0\\Let\ x^2=t\geq 0\\Hence,\\t^2-t+1=0\\D=(-1)^2-4*1*1\\D=1-4\\D=-3\\\\√(D)=√(-3)\\\\ √(D)=i√(3)\ \ \ \ (i=√(-1) ) \\\\t=(1бi√(3) )/(2)\\\\ t=x^2=(1)/(2)бi(√(3) )/(2) \\\\x=б\sqrt{(1-i√(3) )/(2) } \\\\x=б\sqrt{(1+i√(3) )/(2) }`