Question

Find the roots of the given equation x-1/x= 3,x ≠0. *​

Answer 1

your answer is trueAnswer

i)

x−

x

1

=3

⇒x

2

−3x−1=0

⇒x=

2a

−b±

b

2

−4ac

⇒a=1,b=−3,c=−1

⇒x=

2

3±

9+4

⇒x=

2

3±

13

Answer 2

$\huge\color{deeppink}{\colorbox{black}{\cal{【Answer】}}}$

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$\large\bf{\underline{\underline{\green{ \: \: \: \: \: \: \: \: \: \: Question :-}}}}$

Find the roots of the given equation :

x-1/x = 3, x ≠ 0.

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$\large\bf{\underline{\underline{\green{ \: \: \: \: \: \: \: \: \: Solution :-}}}}$

$\sf{∴x - \frac{1}{x} = 3 }$

$\sf{⇝ \frac{ {x}^{2} - 1 }{x} = 3 }$

$\sf{⇝ {x}^{2} - 1 = 3x }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf\boxed{\bold{ \: \: \: \: \: \: \:∴ {x}^{2} - 3x - 1 = 0 \: \: \: \: \: \: }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf{a = 1, \: b = - 3, \: c = - 1}$

$\: \: \: \: \: \: \: \: \: \: \: \: \sf{\large\boxed{\bold{\blue{∴x = \frac{ - b \: ± \sqrt{ {b}^{2} - 4ac } }{2a} }}}}$

$\sf{⇝x = \frac{ - ( -3) \: ± \sqrt{ {( - 3)}^{2} - 4(1)( - 1) } }{2(1)} }$

$\sf{⇝x = \frac{3 \: ± \sqrt{9 + 4} }{2} }$

$\sf{⇝ x = \frac{3 \: ± \sqrt{13} }{2} }$

$\bf\underline{\underline{\pink{∴x = \frac{3 + \sqrt{13} }{2} }}} \: \: \: \: \: or \: \: \: \: \: \: \: \: \bf\underline{\underline{\pink{∴x = \frac{3 - \sqrt{13} }{2} }}}$

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