Solve the equation
Given equation is x 2 + x + 1 2 = 0 .
Any equation of the form a x 2 + b x + c = 0 has the solution
x = − b ± D 2 a
Here, D = b 2 − 4 a c is called the discriminant of the quadratic equation.
Therefore,
x = − 1 ± 1 − 4 × 1 × 1 2 2 × 1 = − 1 ± 1 − 2 2 2
Square-root of 1 − 2 2
Comparing it with a 2 + 2 a b + b 2 , we get
a 2 + b 2 = 1 (1)
And
2 a b = − 2 2 (2)
Further solving these equations, we get
a = 1 , b = − 2 i
Thus, x = − 1 ± ( 1 − 2 ) i 2 .
Given equation is
Any equation of the form
Here,
Therefore,
Square-root of
Comparing it with
And
Further solving these equations, we get
Thus,
