Solve `x^4=25` :
Write in standard form:
This is a quadratic in `x^2` :
This is a difference of two squares:
Applying the zero-product property we get:
`x^2-5=0 => x=+-sqrt(5)`
`x^2+5=0 => x^2=-5 => x=+-isqrt(5)`
Thus the four solutions are `+-sqrt(5),+-isqrt(5)` .**If you are asked only for real solutions, the answer given above is correct**
`x^4 = 25 `
To solve, we will take the forth root of both sides.
`==gt ^4sqrt x^4 = ^4sqrt 25 `
Now we will simplify and take absolute value for x.
`==gt I x I = sqrt5 `
`==gt x = +-sqrt5`
Then, there are two 4th roots for 25 : `-sqrt5, and sqrt5`