Solve the equation `x^(2)+x+(1)/(sqrt(3))=0`

Answer

N/a

Explanation

`x^(2)+x+(1)/(sqrt(3))=0`
`rArr" "sqrt(3)x^(2)+sqrt(3)x+1=0`
Here, `a=sqrt(3), b=sqrt(3), c=1`
Now, from Sridharacharya's formula
`" "x=(-bpmsqrt(b^(2)-4ac))/(2a)`,
`" "x=(-sqrt(3)pmsqrt((sqrt(3))^(2)-4(sqrt(3))(1)))/(2sqrt(3))`
`" "=(-sqrt(3)pmsqrt(3-4sqrt (3)))/(2sqrt(3))`
`" "=(-sqrt(3)pmsqrt( -1( 4sqrt(3)-3)))/(2sqrt(3))`
`" "=(-sqrt(3)pmisqrt(4sqrt(3)-3))/(2sqrt(3))`
Therefore, the roots of the given equation are
`(-sqrt(3)+isqrt(4sqrt(3)-3))/(2sqrt(3)) and (-sqrt(3)-isqrt(4sqrt(3)-3))/(2sqrt(3))`.