Question

What are the solutions to this equation? - 7 + (x^2 - 19)^(3/4) = 20

A) x = 6
B) x = -6
C) x = 18
D) x = -18

Answer 1

The solutions to the equation are x = ± sqrt(27^(4/3) + 19).

Step-by-step explanation:

This equation can be solved by isolating the variable on one side of the equation. So let's start by subtracting 20 from both sides:

-7 + (x^2 - 19)^(3/4) - 20 = 0

Next, we simplify the expression within the parentheses:

(x^2 - 19)^(3/4) = 27

Now, we can raise both sides to the power of 4/3 to eliminate the exponent:

x^2 - 19 = 27^(4/3)

Finally, we can solve for x by adding 19 to both sides and taking the square root:

x^2 = 27^(4/3) + 19

x = ± sqrt(27^(4/3) + 19)

So the solutions to the equation are:

x = ± sqrt(27^(4/3) + 19)