Question

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

Answer 1

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

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

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

$\green{\underline \bold{Given: }} \\ \tt: \implies {x}^{2} - 3x - 1 = 0 \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies value \: of \: x = ?$

• According to given question :

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

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

Answer 2

Answer:(x-$\frac{3+\sqrt{13} }{2}$).(x-$\frac{3-\sqrt{13} }{2}$)

Step-by-step explanation:

first, you need to find Δ= $b^{2}-4ac$ = 13

then get x1,x2=$\frac{3+\sqrt{13} }{2}$, $\frac{3-\sqrt{13} }{2}$

second, the simplify will be (x-$\frac{3+\sqrt{13} }{2}$).(x-$\frac{3-\sqrt{13} }{2}$)