Question

1/x+5 = 1/x^2solve the following quadratic equations.​

Answer 1

Answer:

$\frac{1}{x + 5} = \frac{1}{x {}^{2} } \\ \\ \bf on \: cross - multiplying : \\ \\ x {}^{2} = x + 5 \\ \\ x {}^{2} - x - 5 = 0$

Now,

Here, a = 1, b = -1 , c = -5

D = b² - 4ac

D = (-1)² - 4 * 1 * (-5)

D = 1 + 20

D = 21

$x = \frac{ - b \pm \sqrt{D} }{2a} \\ \\ x = \frac{ - ( -1 ) \pm \sqrt{21} }{2 \times 1} \\ \\ x = \frac{ 1 \pm \sqrt{21} }{2} \\ \\ x = \frac{1 + \sqrt{21} }{2} \: or \: x = \frac{1 - \sqrt{21} }{2}$

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