Question

x^2-4x-7 using shree dharacharya formula​

Answer 1

$\sf \: {x}^{2} - 4x - 7 = 0$

Comparing with ax² + bx + c= 0,

$\sf a = 1 ,b = - 4 , \: c = - 7$

$\sf {b}^{2} - 4ac = ( - 4)^{2} - 4 \times 1 \times - 7$

$\sf = 16 - 4 \times - 7$

$\sf \: = 16 + 28$

$\sf \: {b}^{2} - 4ac= 44$

By Shree Dharacharya Formula -

$\displaystyle \sf \: x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a}$

$\displaystyle \sf \: x = \frac{ - ( - 4) \pm \: \sqrt{44} }{2 \times 1}$

$\displaystyle \sf \: x = \frac{4 \pm \: \sqrt{11 \times 4} }{2}$

$\displaystyle \sf \: x = \frac{4 \pm \:2 \sqrt{11} }{2}$

$\displaystyle \sf \: x = \frac{4 + 2 \sqrt{11} }{2} \: or \: x = \frac{4 - 2 \sqrt{11} }{2}$

$\green{ \displaystyle \sf \: x = 2 + \sqrt{11} \: or \: \: x = 2 - \sqrt{11} }$