Question

√3+√2\√3-√2 + √3-√2\√3+√2 simplify

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

$\tt{\rightarrow\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}}$

$\tt{\rightarrow\dfrac{(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2}})\times\dfrac{(\sqrt{3}+\sqrt{2})}{(\sqrt{3}+\sqrt{2})}}}$

$\tt{\rightarrow\dfrac{(\sqrt{3}+\sqrt{2})^{2}}{(\sqrt{3})^{2}-(\sqrt{2})^{2}}}$

$\tt{\rightarrow\dfrac{(\sqrt{3}+\sqrt{2})^{2}}{3-2}}$

= (√3 + √2)²

= (√3)² + (√2)^2 + 2 × √3 × √2

= 3 + 2 + 2√6

= 5 + 2√6

Now

$\tt{\rightarrow\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}}$

$\tt{\rightarrow\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}\times\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}}}$

$\tt{\rightarrow\dfrac{(\sqrt{3}+\sqrt{2})^{2}}{3-2}}$

= (√3 - √2)²

= (√3)² + (√2)^2 - 2 × √3 × √2

= 3 + 2 - 2√6

= 5 - 2√6

$\tt{\rightarrow\dfrac{(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2}})\times\dfrac{(\sqrt{3}-\sqrt{2})}{(\sqrt{3}+\sqrt{2})}}}$

= 5 + 2√6 + 5 - 2√6

= 10