Find all real solutions of the equation. x^(1/2) - 3 *x^(1/4) = 28?

Answer 1

Let y = x^(1/4)
y ² - 3 y - 28 = 0
(y - 7)(y + 4) = 0
y = 7 , y = - 4
x^(1/4) = 7 , x^(1/4) = (- 4)
x = 7^4 , x= (- 4)^4
x = 2401 , x = 256

Answer 2

x^(1/2) - 3 *x^(1/4) = 28 >> x^(1/2) - 3 *x^(1/4) - 28 = 0
>> (x^(1/4) + 4 ) (x^ (1/4) - 7 ) = 0
(x^(1/4) + 4 ) = 0 it hasn't real answer
(x^1/4 - 7) = 0 >> x^ (1/4) = 7 >> x = 2401
the easier solution is to put u instead of x ^ 1/4 so we have this equation
u ^ 2 - 3 u = 28 it's easy to find the answer of the you after findinf the u you will put x ^ 1/4 instead of u