Question

if 5-root 3 /2+root 3 = x+y root3 find x and y​

Answer 1

Answer:

x = 13 ; y = -7

Step-by-step explanation:

refer the attachment

Answer 2

Given:

$\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = x + y \sqrt{3}.$

To Find:

We have to find out the values of x and y.

Solution:

Given that, $\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = x + y \sqrt{3}.$

Rationalising the denominator of $\frac{5 - \sqrt{3}}{2 + \sqrt{3}}$, we get,

$\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = \frac{5 - \sqrt{3}}{2 + \sqrt{3}} . \frac{2 - \sqrt{3}}{2 - \sqrt{3}}$

$= \frac{(5 - \sqrt{3}) . (2 - \sqrt{3})}{(2^{2} ) - (\sqrt{3})^{2}}$

$= \frac{10 - 5\sqrt{3} - 2\sqrt{3} + (\sqrt{3} )^{2} }{4 - 3}$

$= \frac{13 - 7\sqrt{3}}{1} = 13 - 7\sqrt{3}.$

Replacing $\frac{5 - \sqrt{3}}{2 + \sqrt{3}}$ with $13 - 7\sqrt{3}$ in the given equation, we get,

$13 - 7\sqrt{3} = x + y\sqrt{3}.$

On comparing the L.H.S and R.H.S of the above equation, we get,

$x = 13$ and $y = - 7.$

Hence, the values of x and y in $\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = x + y \sqrt{3}$ are: $x = 13$ and $y = - 7.$

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