Question

If 5+√3/5-√3=x-✓15y please answer x+y​

Answer 1

Answer:

$\red { Value \: of \: x + y }\green {=\frac{ 14 + \sqrt{5}}{11}}$

Step-by-step explanation:

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

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

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

$= \frac{5^{2} - 2\times 5 \times \sqrt{3} + (\sqrt{3})^{2}}{25 - 3}$

$= \frac{ 25 - 10\sqrt{3} + 3}{22}$

$= \frac{28 - 10\sqrt{3}}{22}$

$= \frac{28}{22} - \frac{10\sqrt{3}}{22}$

$= \frac{14}{11} - \frac{5}{11} \sqrt{3}$

$= RHS \\= x - \sqrt{5} \times \sqrt{3} y \:(given)$

$x = \frac{14}{11} \:and \: \sqrt{5}y = \frac{5}{11}$

$x = \frac{14}{11} \:and \: y = \frac{5}{11\times \sqrt{5}}$

$x = \frac{14}{11} \:and \: y = \frac{\sqrt{5}}{11}$

$Now , x + y = \frac{14}{11} + \frac{\sqrt{5}}{11}$

$= \frac{ 14 + \sqrt{5}}{11}$

Therefore.,

$\red { Value \: of \: x + y }\green {=\frac{ 14 + \sqrt{5}}{11}}$

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Answer 2

Answer:

Step-by-step explanation: