QUESTION 5 Given that $$ x=3 $$ and $$ y=3 $$, find the value of Z in the expression; $$ Z^{2}+\frac{8 x}{2 y}=8 $$. (3 marks)

Question

UpStudy AI · Accepted Answer

To find the value of $$ Z $$ in the expression $$ Z^{2} + \frac{8x}{2y} = 8 $$, we will follow these steps:

1. **Substitute the known values**: We know that $$ x = 3 $$ and $$ y = 3 $$. We will substitute these values into the expression.

2. **Simplify the expression**: We will simplify the term $$ \frac{8x}{2y} $$ after substitution.

3. **Solve for $$ Z $$**: We will isolate $$ Z $$ and solve for its value.

Let's start with the substitution:

$$
Z^{2} + \frac{8(3)}{2(3)} = 8
$$

Now, simplify $$ \frac{8(3)}{2(3)} $$:

$$
\frac{8 \cdot 3}{2 \cdot 3} = \frac{24}{6} = 4
$$

Now, substitute this back into the equation:

$$
Z^{2} + 4 = 8
$$

Next, isolate $$ Z^{2} $$:

$$
Z^{2} = 8 - 4
$$
$$
Z^{2} = 4
$$

Finally, take the square root of both sides to find $$ Z $$:

$$
Z = \sqrt{4} = 2 \quad \text{or} \quad Z = -\sqrt{4} = -2
$$

Thus, the possible values of $$ Z $$ are $$ 2 $$ and $$ -2 $$.

The final answer is:
$$
Z = 2 \quad \text{or} \quad Z = -2
$$
$$ Z = 2 $$ or $$ Z = -2 $$

QUESTION 5 Given that \( x=3 \) and \( y=3 \), find the value of Z in the expression; \( Z^{2}+\frac{8 x}{2 y}=8 \). (3 marks)