Question

If a + b$\sqrt{6}$ = $\frac{5+\sqrt{6} }{5-\sqrt{6} }$ , find a,b

Answer 1

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If a + b$\sqrt{6}$ = $\frac{5+\sqrt{6} }{5-\sqrt{6} }$ , , find a,b

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Given:

$\frac{5+\sqrt{6} }{5-\sqrt{6} }$

To find:

Value of a and b.

Let us solve the equation first,

$\frac{5+\sqrt{6} }{5-\sqrt{6} }$ × $\frac{5+\sqrt{6} }{5+\sqrt{6} }$

By using the identity (a+b)² = a²+ 2ab + b² and in the denominator, solving through the identity (a+b) (a-b) = a²-b²

(where a is 5 and b is √6)

25+ 6 + 10√6 / 25-6

31+ 10√6 / 19

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but, 31 + 10$\sqrt{6}$ /19= a + b$\sqrt{6}$

Henceforth, value of a :

$\frac{31}{19}$

and the value of b:

$\frac{10}{19}$

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Answer 2

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