Question

Plzz answer the below question 3

Answer 1

Answer:

a =  21 / 11  and  b = 8 / 11

Hope this helps.

Step-by-step explanation:

The trick is to multiply numerator and denominator by the conjugate of the denominator, as this gets rid of the surds in the denominator.

The denominator is currently 4 - √5.  Its conjugate is 4 + √5.  When you multiply these together you get (difference of squares!)

( 4 - √5 ) ( 4 + √5 ) = 4² - √5² = 16 - 5 = 11.

So putting that into practice....

$\displaystyle\frac{4+\sqrt5}{4-\sqrt5}\\ \\=\frac{(4+\sqrt5)(4+\sqrt5)}{(4-\sqrt5)(4+\sqrt5)} \\ \\=\frac{4^2 + (2)(4)(\sqrt5) + \sqrt5^2}{4^2-\sqrt5^2} \\ \\=\frac{16+5+8\sqrt5}{16-5}\\ \\=\frac{21+8\sqrt5}{11}\\ \\=\tfrac{21}{11}+\tfrac{8}{11}\sqrt5$

Comparing with a + b√5, we get

a =  21 / 11  and  b = 8 / 11