Answer:
The number is 5 or -5.
Explanation:
A number: x
A number to the fourth power: x^4
A number to the fourth power decreased by 600: x^4 - 600
A number to the fourth power decreased by 600 is 25: x^4 - 600 = 25
x^4 - 600 = 25
Subtract 25 from both sides.
x^4 - 625 = 0
Factor as difference of two squares.
(x^2 - 25)(x ^2 + 25) = 0
Factor the left factor as difference of two squares.
(x - 5)(x + 5)(x^2 + 25) = 0
x - 5 = 0 or x + 5 = 0 or x^2 + 25 = 0
x^2 + 25 does not have real solutions.
x = 5 or x = -5