Prove that \(4 - \frac{3}{7}\sqrt{2}\) is an irrational number.
Answer variants:
\(\frac{7}{3}\left(\frac{4q - p}{q}\right) = \sqrt{2}\)
cannot be expressed as p/q form
\(\frac{7}{3}\left(\frac{4q - p}{q}\right)\) is rational
contradicts
co-primes
satisfies
rational Number
can be expressed as p/q form
irrational Number
\(4 - \frac{3}{7}\sqrt{2} = \frac{p}{q}\)
composites
Let's prove is an irrational number.
Now prove by contradiction method.
| 1. | Assume is a | |
| 2. | By the definition, | |
| 3. | And \(p\) and \(q\) are | |
| 4. | So we can write it as | |
| 5. | Simplifying the term, | |
| 6. | This implies that, | |
| 7. | This | our assumption. |
| 8. | Thus, is |