Simplify \(\frac{1}{3-√2}\) in the form of p + q√2
MATHEMATICS
JAMB 2022
Simplify \(\frac{1}{3-√2}\) in the form of p + q√2
- A. \(\frac{7}{3}\) - \(\frac{1}{7?2}\)
- B. \(\frac{7}{3}\) + \(\frac{1}{7?2}\)
- C. \(\frac{3}{7}\) - \(\frac{1}{7?2}\)
- D. \(\frac{3}{7}\) + \(\frac{?2}{7}\)
Correct Answer: D. \(\frac{3}{7}\) + \(\frac{?2}{7}\)
Explanation
Rationalization with conjugate \({3+√2}\)
\(\frac{1}{3-√2}\)
→ \(\frac{1 * [3+√2]}{[3-√2][3+√2]}\)
= \(\frac{3+√2}{9 -3√2 + 3√2 + √4}\)
= \(\frac{3+√2}{9 - 2}\) → \(\frac{3+√2}{7}\)
= \(\frac{3}{7}\) + \(\frac{√2}{7}\)
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *