Question

If x=root 5 + root 3 / root 5- root 3
and y= root 5- root 3/ root 5+ root 3
, find the value of x+y+xy.

I will give 100 points answer fast

Answer 1

Answer:

HOPE THIS WILL HELP YOU

Answer 2

Answer:

The value of the given expression is

$x + y + xy = \frac{39}{11}$

Step-by-step explanation:

The given values of variables are

$x = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$

and

$y = \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} }$

We are required to find the value of x+y+xy.We shall do it by parts

$xy = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } = 1$

And the remaining expression is

$x + y = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } + \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ = \frac{(5 + \sqrt{3} ) {}^{2} + (5 - \sqrt{3} ) {}^{2} }{(5 + \sqrt{3})(5 - \sqrt{3}) } \\ = \frac{2(5 {}^{2} + 3) }{5 {}^{2} - 3 } = \frac{2 \times 28}{22} = \frac{28}{11}$

Therefore,the value of the final expression is

$x + y + xy = \frac{28}{11} + 1 = \frac{39}{11}$

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