Question

2^x^2:2^x=8:1
solve the equation
quadratic equations ​

Answer 1

Step-by-step explanation:

We have,

$\huge{ \frac{ {2}^{ {x}^{2} } }{ {2}^{x} } } = \frac{8}{1}$

$\huge{ \implies {2}^{ {x}^{2} - x }} = {2}^{3}$

$\huge{ \implies {x}^{2} - x } = 3$

$\huge{ \implies {x}^{2} - x - 3 = 0}$

$\huge{ \implies x = \frac{ - ( -1 ) \pm \sqrt{( - 1)^{2} - 4(1)( - 3)} }{2(1)} }$

$\huge{ \implies x = \frac{1 \pm \sqrt{1 + 12} }{2} }$

$\huge{ \implies x = \frac{1 \pm \sqrt{13} }{2} }$

$\huge{ \implies x = \frac{1 + \sqrt{13} }{2} \: \: \: \: \: or \: \: \: \: \: x = \frac{1 - \sqrt{13} }{2} }$