Question

1/x+5=1/x^2 solve quadratic equation

Answer 1

Given:

Quadratic equation 1/x + 5 = 1/x^2

To find:

Solve the quadratic equation.

Solution:

From given, we have a quadratic equation:

1/x + 5 = 1/x^2

First, we need to reduce the given equation in standard form.

multiply both sides by x², we get,

x² × 1/x + x² × 5 = x² × 1/x^2

x + 5x² = 1

5x² + x - 1 = 0

Now, the given equation is in standard form.

where, a = 5, b = 1 and c = -1

we use the below formula to find the roots of a quadratic equation.

$x=\dfrac{-b\pm \sqrt {b^2-4ac}}{2a}$

x = [ -1 ± √ (1² - 4 × 5 × (-1) ] / [ 2 × 5 ]

x = [ -1 ± √21 ] / 10

Therefore, x = (-1 + √21)/10 , x = (-1 - √21)/10