Question

how to solve this question​

Answer 1

$\large{\underline{\rm{Solution:}}}$

$\sf{\implies \dfrac{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}{7-2\sqrt{5}}}$

$\sf{\implies \dfrac{(\sqrt{3})^{2}-(\sqrt{5})^{2}}{7-2\sqrt{5}}}$

$\sf{\implies \dfrac{3-5}{7-2\sqrt{5}}}$

$\sf{\implies \dfrac{-2}{7-2\sqrt{5}}}$

$\underline{\sf{Now,\;we\;will\;do\;rationalize,}}$

$\sf{\implies \dfrac{-2}{7-2\sqrt{5}}\times \dfrac{7+2\sqrt{5}}{7+2\sqrt{5}}}$

$\sf{\implies \dfrac{-2(7+2\sqrt{5})}{(7-2\sqrt{5})(7+2\sqrt{5})}}$

$\sf{\implies \dfrac{-14-4\sqrt{5}}{(7)^{2}-(2\sqrt{5})^{2}}}$

$\sf{\implies \dfrac{-14-4\sqrt{5}}{49-20}}$

$\sf{\implies \dfrac{-14-4\sqrt{5}}{29}}$