Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

If [tex]x = 9 - 4 \sqrt{5}[/tex], find the value of [tex]x^2 + \frac{1}{x^2}[/tex].

Sagot :

GinnyAnswer
Sure, let's find the value of [tex]\( x^2 + \frac{1}{x^2} \)[/tex] given [tex]\( x = 9 - 4 \sqrt{5} \)[/tex].

### Step-by-Step Solution

1. Calculate [tex]\( x \)[/tex]:
- Given [tex]\( x = 9 - 4 \sqrt{5} \)[/tex].

2. Calculate [tex]\( x^2 \)[/tex]:
- We raise [tex]\( x \)[/tex] to the power of 2.
- This gives [tex]\( x^2 = (9 - 4 \sqrt{5})^2 \)[/tex].
- Evaluating this expression, we get [tex]\( x^2 \approx 0.00310562001514181 \)[/tex].

3. Calculate [tex]\( \frac{1}{x^2} \)[/tex]:
- We take the reciprocal of [tex]\( x^2 \)[/tex].
- Therefore, [tex]\( \frac{1}{x^2} \approx \frac{1}{0.00310562001514181} = 321.9968943799899 \)[/tex].

4. Calculate [tex]\( x^2 + \frac{1}{x^2} \)[/tex]:
- Add [tex]\( x^2 \)[/tex] and [tex]\( \frac{1}{x^2} \)[/tex].
- [tex]\( x^2 + \frac{1}{x^2} = 0.00310562001514181 + 321.9968943799899 = 322.00000000000506 \)[/tex].

### Final Answer
The value of [tex]\( x^2 + \frac{1}{x^2} \)[/tex] is approximately [tex]\( 322.00000000000506 \)[/tex].
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.