Question

17........................

Answer 1

Answer:

a. $0.76,-0.76$

Step-by-step explanation:

The given equation is;

$-8=-3-6\sqrt[3]{x^2}$

Add 3 to both sides of the equation to get;

$-8+3=-3+3-6\sqrt[3]{x^2}$

$\Rightarrow -5=-6\sqrt[3]{x^2}$

Divide both sides by -6.

$\Rightarrow \frac{-5}{-6}=\sqrt[3]{x^2}$

$\Rightarrow \frac{5}{6}=\sqrt[3]{x^2}$

Cube both sides of the equation;

$\Rightarrow (\frac{5}{6})^3=x^2$

$\Rightarrow \frac{125}{216}=x^2$

Take square root of both sides

$\pm \sqrt{\frac{125}{216}}=x$

$\pm 0.76=x$

$\therefore x=0.76,-0.76$

Answer 2

Answer:

Step-by-step explanation:

First, add 3 to both sides:

-5 = -6∛(x²)

Next, divide both sides by -6, to isolate ∛(x²):

5/6 = ∛(x²)

Eliminate the radical by cubing both sides:

5³

---- = x²

6³

Finally, take the square root of both sides.  This will isolate x.  There will be two roots:  one +, the other -.

x = ±√(5³/6³)

This simplifies to:  ± (5/6)∛(5/6).