Question

4 + root 5 divided by 4 minus 5 is equal to a + b root 5 find the value of a and b​

Answer 1

$\frac{4 + \sqrt{5} }{4 - \sqrt{5} } = a + b \sqrt{5}$

Rationalise the denominator

$\frac{4 + \sqrt{5} }{4 - \sqrt{5} } \times \frac{4 + \sqrt{5} }{4 + \sqrt{5} } \\ = > \frac{( {4 + \sqrt{5} })^{2} }{( {4})^{2} - ( { \sqrt{5} })^{2} } \\ = > \frac{16 + 5 + 8 \sqrt{5} }{16 - 5} \\ = > \frac{21 + 8 \sqrt{5} }{11}$

We write this as :

$= > \frac{21}{11} + \frac{8 \sqrt{5} }{11 }$

Now compare with

$a + b \sqrt{5}$

we get ,

$a = \frac{21}{11}$

and

$b = \frac{8}{11}$

hope this helps you

Answer 2

Answer:

a= 21/11 and b= 8/11

hope this answer will help you.

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