Question

Solve the following quadratic equation.

`1/(x + 5) = 1/x^2`

Answer 1

`1/(x + 5) = 1/x^2`

∴ x² = x + 5

∴ x² − x − 5 = 0

Comparing the above equation with ax² + bx + c = 0, we get,

a = 1, b = −1, c = −5

∴ b² − 4ac = (−1)² − 4 × 1 × −5 = 1 + 20 = 21

`x = (-b +- sqrt(b^2 - 4ac))/(2a)`

`x = (-(-1) +- sqrt(21))/(2 × 1)`

`x = (1 +- sqrt(21))/(2)`

`x = (1 + sqrt(21))/(2) or x = (1 - sqrt(21))/2`

∴ The roots of the given quadratic equation are `(1 + sqrt(21))/(2) "and" (1 - sqrt(21))/2`.