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

Answer

N/a

Explanation

Given equaton is `x ^(2) +x+(1)/(sqrt(2))=0`
Here, `A=1, B =1, C=(1)/(sqrt(2))`
Discriminant `D=B^(2)-4 AC`
`" "=(1)^(2)- 4xx1xx(1)/(sqrt(2)) `
`" "=1-2xxsqrt(2)xxsqrt(2)xx(1)/(sqrt(2)) `
`" "=1-2sqrt(2)`
`therefore" "x=(-Bpmsqrt(D))/(2A)`
`rArr" "x=(-1pmsqrt(-(2sqrt(2)-1)))/(2)`
`" "=(-1pmsqrt((2sqrt(2)-1)i^(2)) ) /(2)`
`rArr" "x=(-1pmisqrt(2sqrt(2) -1))/(2)`
Therefore, solutions of equation are
`" "x=(-1pmisqrt(2sqrt(2)- 1))/(2)`