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Simplifyx^2-3x-1PLEASE ANSWER FAST.......

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\blue{\bold{\underline{\underline{Answer:}}}}

\green{\tt{\therefore{x = \frac{3 \pm \sqrt{13} }{2}}}}\\

\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}

\green{\underline \bold{<klux>GIVEN</klux>: }} \\ \tt: \implies {x}^{2} - 3x - 1 = 0 \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies value \: of \: x = ?

• ACCORDING to given QUESTION :

\tt: \implies {x}^{2} - 3x - 1 = 0 \\ \\ \tt \circ \: a = 1 \\ \\ \tt \circ \: b = - 3 \\ \\ \tt \circ \: c = - 1\\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies D= {b}^{2} - 4ac \\ \\ \tt: \implies D = {( - 3)}^{2} - 4 \times 1 \times ( - 1) \\ \\ \tt: \implies D = 9 + 4 \\ \\ \tt: \implies D= 13 \\ \\ \tt: \implies x = \frac{ - b \pm \sqrt{D} }{2a} \\ \\ \tt: \implies x = \frac{ - ( - 3) \pm \sqrt{13} }{2 \times 1} \\ \\ \green{\tt: \implies x = \frac{3 \pm \sqrt{13} }{2} }

\bold{Alternate \: method} \\ \tt: \implies {x}^{2} - 3x - 1 = 0 \\ \\ \tt Both \: side \: adding \: (\frac{b}{2a})^{2} = (\frac{ - 3}{2 \times 1} )^{2} = \frac{9}{4} \\ \\ \tt: \implies {x}^{2} - 3x + \frac{9}{4} - 1 = \frac{9}{4} \\ \\ \tt: \implies {(x - \frac{3}{2}) }^{2} = \frac{9}{4} + 1 \\ \\ \tt: \implies {(x - \frac{3}{2} )}^{2} = \frac{9 + 4}{4} \\ \\ \tt: \implies x - \frac{3}{2} = \sqrt{ \frac{13}{4} } \\ \\ \tt: \implies x - \frac{3}{2} = \pm \frac{13}{2} \\ \\ \green{\tt: \implies x = \frac{3 \pm \sqrt{13} }{2} }


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