Question

how do you solve x^4-625 = 0

Answer 1

you can start by substituting \(x^2=u\)

Answer 2

then solve for "u" (2 values) and then for "x" (2 values for each x, so four values in all)

Answer 3

It can be written as:

\[(x^2)^2 - (25)^2= = 0\]

And you can use:

\[x^2 - y^2 = (x-y)(x+y)\]

Answer 4

(x-5)(x+5)

Answer 5

Look it carefully and tell where it is x or x^2??

Answer 6

try making it simpler
\[u^2-625=0\\
\implies u=\pm\sqrt{625}=\pm25\\
x^2=25\qquad\qquad \boxed{x^2=-25}\;\text{(no real solutions, imaginary)}\\
\boxed{x = \pm 5}
\]

Answer 7

Then is it: (x^2+5)(x^2-5)

Answer 8

No, that is 25^2 so, It would be 25.

Answer 9

\[(x^2)^2 - (25)^2= 0 \implies (x^2 - 25)(x^2 + 25) = 0\]

Answer 10

lets make it even simple
\[zx^4-625=(x-25)(x+25)=(x-5)(x+5)(x^2+25)\]

Answer 11

*x^2 @satellite73