solve using quadratic formula

Question

find all complex number solutions

 

 

1

--

x to the second power - 3 = 8

                                         --

                                          x

Answer 1

is this 1/x² - 3/x = 8?

 

If so...

 

Multiply both sides by x².  (This is only OK if x is not 0, but we know that because if it were then the whole equation would be invalid, because there are terms that have x in the denominator, which is not allowed if x is 0.)

 

1 - 3x = 8x²

0 = 8x² + 3x - 1

 

Use the quadratic formula:

 

x = (-b ± √(b²-4ac)) / 2a

 

x = (-3 ± √(9 -4*8*(-1))) / 16

x = (-3 ± √41) / 16

 

So the solutions are:

(-3 + √41) / 16

(-3 - √41) / 16