Question

rationalizati numitorul raportului 1 supra √2+√3-√5

Answer 1

O sa folosim formula (a - b)(a + b), unde a = √2 + √3, si b = √5

$\frac{1}{\sqrt{2}+\sqrt{3}-\sqrt{5}}=\frac{( \sqrt{2}+\sqrt{3})-\sqrt{5}}{( \sqrt{2}+ \sqrt{3} )^2-5}=\frac {\sqrt{2}+\sqrt{3}-\sqrt{5}}{2+2 \sqrt{6} +3-5} = \frac{ \sqrt{2}+\sqrt{3}-\sqrt{5}}{2 \sqrt{6} }= \frac{2\sqrt{3}+3\sqrt{2}-\sqrt{30}}{2}$