Question

Is the equation 5−5⋅(5–√3)12=15
true or false? Enter 1 for true or 2 for false.(1 point)

Answer 1

To evaluate the expression \(5 - 5 \cdot (5 - \sqrt{3})^{12}\) and see if it equals 15, we can simplify it step by step.

1. Calculate \(5 - \sqrt{3}\):
- This is a numerical value, approximately \(5 - 1.732 = 3.268\).

2. Raise \(3.268\) to the 12th power, which is a very large number:
- However, we will keep it as \((5 - \sqrt{3})^{12}\) for now.

3. Multiply by 5:
- This results in \(5 \cdot (5 - \sqrt{3})^{12}\).

4. Subtract from 5:
\[
5 - 5 \cdot (5 - \sqrt{3})^{12}
\]

Since \((5 - \sqrt{3})^{12}\) is a positive number (as both \(5\) and \(\sqrt{3}\) are positive), multiplying by \(5\) gives us a very large positive number. Thus, \(5 - 5 \cdot (5 - \sqrt{3})^{12}\) will yield a negative number.

Now we can conclude that \(5 - 5 \cdot (5 - \sqrt{3})^{12} \neq 15\).

Therefore, the answer is **2 (false)**.