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
\(\frac{3}{7}\) + \(\frac{√2}{7}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Rationalization with conjugate \({3+√2}\)
\(\frac{1}{3-√2}\)
→ \(\frac{1 * [3+√2]}{[3-√2][3+√2]}\)
= \(\frac{3+√2}{9 -3√2 + 3√2 - √4}\)
= \(\frac{3+√2}{9 - 2}\) → \(\frac{3+√2}{7}\)
= \(\frac{3}{7}\) + \(\frac{√2}{7}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #64209)