Simplify frac 1 3- 2 in the form of p q 2 - JAMB Mathematics 2022 Question
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 option: d
Rationalizing the denominator using conjugates with the numerator an integer, \({3+√2}\)
\(\frac{1}{3-√2}\)
=> \(\frac{1 * [3+√2]}{[3-√2][3+√2]}\)
= \(\frac{3+√2}{9 -3√2 + 3√2 + √4}\)
= \(\frac{3+√2}{9 - 2}\) → \(\frac{3+√2}{7}\)
= \(\frac{3}{7}\) + \(\frac{√2}{7}\)
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