Question

solve x^8-x^5+x^3-1=0

Answer 1

Answer:

1 answer is this equation 0.16

Answer 2

${x}^{8} - {x}^{5} + {x}^{3} - 1 = 0$

${x}^{5} ( {x}^{3} - 1) + ( {x}^{3} - 1) = 0$

$( {x}^{3} - 1)( {x}^{5} + 1) = 0$

Therefore, the eight solutions are:

$x _1 = 1$

$x_{2} = - \frac{1}{2} + \frac{ \sqrt{ 3} }{2} i$

$x_{ 3 } = - \frac{1}{2} - \frac{ \sqrt{ 3 } }{2} i$

$x_{4} = - 1$

$x_5 = \frac{ 1 - \sqrt{5} }{4} + \frac{ \sqrt{ 10 + 2 \sqrt{5} } }{4} i$

$x_6 = \frac{1 - \sqrt{5} }{4} - \frac{ \sqrt{ 10 + 2 \sqrt{5} } }{4} i$

$x_7 = \frac{ 1 + \sqrt{5} }{4} + \frac{ \sqrt{ 10 - 2 \sqrt{5} } }{4} i$

$x_8 = \frac{1 + \sqrt{5} }{4} - \frac{ \sqrt{ 10 - 2 \sqrt{5} } }{4} i$

where,

$i = \sqrt{ - 1}$