Question

solve by using quadratic formula x2-3x+1=0​

Answer 1

Answer:

${x}^{2} - 3x + 1 = 0 \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \\ a = 1 \\ b = - 3 \\ c = 1 \\ \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{ - ( - 3)± \sqrt{ {( - 3)}^{2} - 4 \times 1 \times1 } }{2 \times 1} \\ x = \frac{3± \sqrt{9 - 4} }{2} \\ x= \frac{3± \sqrt{5} }{2} \\ \large{ \boxed{x = \underline{ \underline{\frac{3 + \sqrt{5} }{2} }} \: \: \: or \: \: \: \underline{ \underline{\frac{3 - \sqrt{5} }{2}}}}}$

Answer 2

GivEn EquAtiOn :-

• x² - 3x + 1 = 0

To SolVe :-

• by using Quadratic Formula

QuaDraTiC ForMulAe :-

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

$\sf\bigstar{ \: For \: an \: Equation \: a {x}^{2} + bx + c = 0}$

SoLuTioN :-

Here,

• a = 1
• b = -3
• c = 1

Now, By using the Above Formulae,

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

$\sf{x = \frac{ 3 ± \sqrt{ 9 - 4 }}{2} }$

$\sf{x = \frac{ 3 ± \sqrt{ 5 }}{2} }$

Which is your required answer!!

Therefore,

$\sf\blue{x = \frac{ 3 + \sqrt{ 5 }}{2} \: and \: \frac{3 - \sqrt{5} }{2} } \: \: \underline{Answer.}$