Answer:
the solutions to the equation -7 + (x^2-19)^(3/4) = 20 are x = 10 and x = -10.
Explanation:
To solve the equation -7 + (x^2-19)^(3/4) = 20, we can follow these steps:
Add 7 to both sides of the equation to isolate the radical term:
(x^2-19)^(3/4) = 27
Raise both sides of the equation to the power of 4/3 to cancel out the radical:
[(x^2-19)^(3/4)]^(4/3) = 27^(4/3)
x^2 - 19 = 81
Add 19 to both sides of the equation to isolate the variable:
x^2 = 100
Take the square root of both sides of the equation:
x = ±10
Therefore, the solutions to the equation -7 + (x^2-19)^(3/4) = 20 are x = 10 and x = -10.