17. Solve 3x² – 3x⁰•⁵ =8
The given equation is 3x² - 3x^0.5 = 8.
To solve this equation, we need to isolate the term with x² on one side of the equation. Let's begin.
First, we need to simplify the equation:
3x² - 3√x = 8.
Next, let's move the term with square root (√x) to the other side of the equation:
3x² = 8 + 3√x.
Now, let's isolate x² by subtracting the term with √x from both sides:
3x² - 3√x = 8 + 3√x - 3√x,
3x² - 3√x = 8.
Simplifying the equation further gives:
3x² = 8.
Finally, divide both sides of the equation by 3 to solve for x:
x² = 8/3.
Taking the square root of both sides gives the two possible solutions:
x = ±√(8/3).
Hence, the solutions to the equation 3x² - 3x^0.5 = 8 are x = ±√(8/3).