JAMB - Mathematics (1997 - No. 5)
Simplify \(\frac{2\sqrt{3} + 3\sqrt{5}}{3\sqrt{5} - 2\sqrt{3}}\)
\(\frac{19 + 4\sqrt{25}}{11}\)
\(\frac{19 + 4\sqrt{15}}{11}\)
\(\frac{19 + 2\sqrt{15}}{11}\)
\(\frac{19 + 2\sqrt{15}}{19}\)
Explicação
\(\frac{(2\sqrt{3} + 3\sqrt{5})(3\sqrt{5} + 2\sqrt{3})}{(3\sqrt{5} - 2\sqrt{3})(3\sqrt{5} - 2\sqrt{3})}\)
= \(\frac{57 + 12\sqrt{15}}{33}\)
=\(\frac{19 + 4\sqrt{15}}{11}\)
= \(\frac{57 + 12\sqrt{15}}{33}\)
=\(\frac{19 + 4\sqrt{15}}{11}\)