Question

If 5+√3/5-√3=x-✓15y please answer x+y

Answer 1

The value of $x+y$ is "$\dfrac{14+\sqrt{5} }{11}$".

Step-by-step explanation:

We have,

$\dfrac{5+\sqrt{3} }{5-\sqrt{3}} =x-\sqrt{15} y$

Conjugate, we get

⇒ $\dfrac{5+\sqrt{3} }{5-\sqrt{3}}\times \dfrac{5+\sqrt{3} }{5+\sqrt{3}} =x-\sqrt{15} y$

⇒$\dfrac{25+3+10\sqrt{3} }{25-3} =x-\sqrt{15} y$

⇒ $\dfrac{28+10\sqrt{3} }{22} =x-\sqrt{15} y$

⇒$\dfrac{28}{22}+\dfrac{10\sqrt{3} }{22} =x-\sqrt{15} y$

⇒ $\dfrac{14}{11}+\dfrac{5\sqrt{3} }{11} =x-\sqrt{15} y$

⇒ $\dfrac{14}{11}+\dfrac{\sqrt{5} \sqrt{15} }{11} =x-\sqrt{15} y$

Equating both sides, we get

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

∴$x+y=</strong>\dfrac{14}{11}+\dfrac{\sqrt{5} }{11}=<strong>\dfrac{14+\sqrt{5} }{11}$

Hence, the value of $x+y$ is $\dfrac{14+\sqrt{5} }{11}.$