Question

Find the roots of the quadratic equation
(x2 + 1)2 - x2 = 0​

Answer 1

Step-by-step explanation:

${( {x}^{2} + 1)}^{2} - {x}^{2} = 0 \\ ( {x}^{2} + 1 + x)( {x}^{2} + 1 - x) = 0 \\ {x}^{2} + x + 1 = 0 \: \: or \: \: {x}^{2} - x + 1 = 0 \\ from \: eq1 \\ {x}^{2} + x + 1 = 0 \\ x = \frac{ - 1 + \sqrt{ - 3} }{2} ,x = \frac{ - 1 - \sqrt{ - 3} }{2}$

$from \: eq2 \\ {x}^{2} - x + 1 = 0 \\ x = \frac{ 1 + \sqrt{ - 3} }{2} ,x = \frac{ 1 - \sqrt{ - 3} }{2}$

$roots \: of \: eq \: are \\ x = \frac{ - 1 + \sqrt{ - 3} }{2} ,x = \frac{ - 1 - \sqrt{ - 3} }{2} \\ x = \frac{ 1 + \sqrt{ - 3} }{2} ,x = \frac{ 1 - \sqrt{ - 3} }{2}$