`x^(4) + 1 = 0` के सभी मूलों को निकालें |

Explanation

`x^(4) + 1 = 0`
`implies x^(4) + 2x^(2) + 1 - 2x^(2) = 0`
`implies (x^(2) + 1)^(2) - (sqrt(2x)^(2) = 0`
`implies (x^(2) + 1 + sqrt2x) ( x^(2) + 1 - sqrt2x) = 0`
अब `x^(2) + sqrt2x + 1 = 0 implies x = (-2 pm sqrt(2 - 4) )/(2) = (-sqrt pm (sqrt-2))/(2)`
`therefore x = (- sqrt2 pm sqrt2 i)/(2) = (-1 pm i)/(sqrt2)`
पुरा `x^(2) - sqrt2x + 1 = 0`
`implies x = (sqrt2 pm sqrt(2 -4 ))/(2) = (sqrt2 pm sqrt-2)/(2) = (sqrt2 pm sqrt2i)/(2) = (1 pm i)/(sqrt2)`
अतः `x^(4) + 1` के सभी मूल `(-1 pm i)/(sqrt2) , (1 pm i)/(sqrt2)` है |