Question

find the roots of the following square equation by factorization
$\frac{x + 1}{x - 1} - \frac{x - 1}{x + 1?} = \frac{5}{6} \:$

Answer 1

HEYA!
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✴ROOTS OF A QUADRATIC EQUATION✴
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$\frac{x + 1}{x - 1} - \frac{x - 1}{x + 1} = \frac{5}{6 } \\ \\ = \frac{(x + 1) {}^{2} - (x - 1) {}^{2} }{(x - 1)(x + 1)} = \frac{5}{6} \\ \\ = \frac{ x{}^{2} +1 + 2x - (x {}^{2} + 1 - 2x)}{(x - 1)(x + 1)} = \frac{5}{6} \\ \\ = \frac{x {}^{2} + 1 + 2x - x {}^{2} - 1 + 2x }{(x - 1)(x + 1)} = \frac{5}{6 } \\ \\ = \frac{4x}{x {}^{2} - 1} = \frac{5}{6} \\ \\ = > 24x = 5x {}^{2} - 5 \\ \\ = > 24x - 5x {}^{2} + 5 = 0 \\ \\ = > 5x {}^{2} - 24x - 5 = 0 \\ \\ using \: quadratic \: formula \\ \\ x = \frac{ - b \frac{ + }{ - } \sqrt{b {}^{2} - 4ac} }{2a} \\ \\ a = 5 \: \: \: \: \: b = - 24 \: \: c = - 5 \\ \\ \\ discriminant \: d = \sqrt{ b {}^{2} - 4ac } \\ \\ = \sqrt{576 - 4 \times 5 \times - 5} = \sqrt{676} = 26 \\ \\ x = \frac{24 + 26}{10} = \frac{50}{10} = 5 \\ \\ x = \frac{24 - 26}{10} = \frac{ - 2}{10} = \frac{ - 1}{5}$

Hence the roots are -1/5 and 5 . It has real and distinct roots .

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