Question

simplify
x=9±2√3 over 2

Answer 1

To simplify the expression \( x = \frac{9 \pm 2\sqrt{3}}{2} \), we can separate the two cases for the plus and minus:

1. For the case with the plus sign:
\[
x_1 = \frac{9 + 2\sqrt{3}}{2}
\]

2. For the case with the minus sign:
\[
x_2 = \frac{9 - 2\sqrt{3}}{2}
\]

Now, we can simplify each case further:

### Case 1: \( x_1 = \frac{9 + 2\sqrt{3}}{2} \)
\[
x_1 = \frac{9}{2} + \frac{2\sqrt{3}}{2} = \frac{9}{2} + \sqrt{3}
\]

### Case 2: \( x_2 = \frac{9 - 2\sqrt{3}}{2} \)
\[
x_2 = \frac{9}{2} - \frac{2\sqrt{3}}{2} = \frac{9}{2} - \sqrt{3}
\]

Thus, the simplified versions of \( x \) are:
\[
x_1 = \frac{9}{2} + \sqrt{3} \quad \text{and} \quad x_2 = \frac{9}{2} - \sqrt{3}
\]

So, the final simplified form of the expression \( x \) can be written as:
\[
x = \frac{9}{2} \pm \sqrt{3}
\]