Question

plz answer it.
simplify it.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$\frac{42}{11}$

Step-by-step explanation:

Given :

To find the value of,

$\frac{4 + \sqrt{5} }{4-\sqrt{5} } + \frac{4 - \sqrt{5} }{4+\sqrt{5} }$

Solution :

By cross-multiplication,

$\frac{4 + \sqrt{5} }{4-\sqrt{5} } + \frac{4 - \sqrt{5} }{4+\sqrt{5} }$

$\frac{(4+\sqrt{5})(4+\sqrt{5}) + (4-\sqrt{5})(4-\sqrt{5})}{(4+\sqrt{5})(4-\sqrt{5})}$

By breaking down processes ,

In numerator,

$(4+\sqrt{5})(4+\sqrt{5}) = 16 + 5 + 8\sqrt{5}$

$(4-\sqrt{5})(4-\sqrt{5}) = 16 + 5 - 8\sqrt{5}$

$(4+\sqrt{5})(4+\sqrt{5}) + (4-\sqrt{5})(4-\sqrt{5}) = 16 + 5 + 8\sqrt{5} + 16 + 5 - 8\sqrt{5} = 42 + 8\sqrt{5} - 8\sqrt{5} = 42$

In denominator,

$(4+\sqrt{5})(4-\sqrt{5}) = 16 - 5 = 11$

Hence,

$\frac{(4+\sqrt{5})(4+\sqrt{5}) + (4-\sqrt{5})(4-\sqrt{5})}{(4+\sqrt{5})(4-\sqrt{5})}= \frac{42}{11}$

∴ $\frac{4 + \sqrt{5} }{4-\sqrt{5} } + \frac{4 - \sqrt{5} }{4+\sqrt{5} } =\frac{42}{11}$