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justaguide eNotes educator| Certified Educator

The equation x^4=625 has to be solved.

x^4=625

=> x^2 = 25 and x^2 = -25

=> x = 5, x = -5 and x = -5i, x = 5i

The solution of the equation x^4 = 625 is {-5i, 5i, -5, 5}

givingiswinning | Student

(x^2+25)(x^2 - 25)

x^2 + 25 =0

`x = +- 5i`

x^2 - 25 =0

`x = +-5`

atyourservice | Student

x^4=625

x^4 - 625

use the difference of 2 squares:

(x^2+25)(x^2 - 25)

set them equal to 0

x^2 + 25 =0

x = +- 5i

x^2 - 25 =0

x = +-5

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