Question

Find the value of a and b in root 6 plus root 5 upon root 6 minus root 5 is equal to a plus b root 5

Answer 1

Hey mate!

✴ RATIONALISATION ✴

$\frac{ \sqrt{6} + \sqrt{5} }{ \sqrt{6} - \sqrt{5} } = a + b \sqrt{30} \\ \\ \frac{ \sqrt{6} + \sqrt{5} }{ \sqrt{6} - \sqrt{5} } \times \frac{ \sqrt{6} + \sqrt{5} }{ \sqrt{6} + \sqrt{5} } \\ \\ \frac{( \sqrt{6} + \sqrt{5}) {}^{2} }{( \sqrt{6} ) {}^{2} - ( \sqrt{5}) {}^{2} } \\ \\ \frac{6 + 2 \sqrt{30} + 5}{6 - 5} \\ \\ 11 + 2 \sqrt{30}$

Therefore, a = 11 and b = 2


Thanks for the question!

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