Question

x + 1/x = -2 so x = ?

please provide detail steps and same example with other negative and positive digits. ​

Answer 1

$\huge \fcolorbox{red}{blue}{ \bf \color{maroon}{x = - 1}}$

Step-by-step explanation:

$\bf x + \frac{1}{x } = - 2$

[Now multiply the equation by x]

$\\ = > \bf x \times (x + \frac{1}{x} = - 2) \\ \\ = > \bf (x \times x) + ( \cancel{x} \times \frac{1}{ \cancel{x}} ) = ( - 2 \times x) \\ \\ = > \bf {x}^{2} + 1 = - 2x \\ \\ = > \bf {x}^{2} +2x + 1 = 0$

Now, we can solve the quadratic equation by any method, (let's solve with factorisation method)

$\\ = >\bf {x}^{2} + 2x + 1 = 0 \\ \\ = > \bf {x}^{2} + x + x + 1 = 0 \\ \\ = > \bf x(x + 1) + 1(x + 1) = 0 \\ \\ = > \bf (x + 1)(x + 1) = 0$

So,

value of x -

First case -

x + 1 = 0

=> x = - 1

In second case -

x + 1 = 0

=> x = - 1

.

So,

the value of x is - 1.

Hope it helps.