JAMB - Mathematics (2022 - No. 7)

Simplify \(\frac{1}{3-√2}\) in the form of p + q√2

\(\frac{7}{3}\) - \(\frac{1}{7√2}\)

\(\frac{7}{3}\) + \(\frac{1}{7√2}\)

\(\frac{3}{7}\) - \(\frac{1}{7√2}\)

\(\frac{3}{7}\) + \(\frac{√2}{7}\)

Rationalization with conjugate \({3+√2}\)

\(\frac{1}{3-√2}\)

→ \(\frac{1 * [3+√2]}{[3-√2][3+√2]}\)

= \(\frac{3+√2}{9 -3√2 + 3√2 - √4}\)

= \(\frac{3+√2}{9 - 2}\) → \(\frac{3+√2}{7}\)

= \(\frac{3}{7}\) + \(\frac{√2}{7}\)