Question

Solve the equation

Answer 1

Given equation is x 2 +x+ 1 2 =0 .

Any equation of the form a x 2 +bx+c=0 has the solution

x= −b± D 2a

Here, D= b 2 −4ac 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 +2ab+ b 2 , we get

a 2 + b 2 =1 (1)

And

2ab=−2 2 (2)

Further solving these equations, we get

a=1,b=− 2 i

Thus, x= −1±( 1− 2 )i 2 .