Question

Considere a igualdade raiz de 75 - raiz de 24 = 1/x raiz de 3. Qual o valor de X ?

Answer 1

$\sqrt{75}-\sqrt{24}=\dfrac{1}{x\sqrt{3}}\\\\\\\sqrt{3.5.5}-\sqrt{2.2.2.3}=\dfrac{1}{x\sqrt{3}}\\\\\\x=\dfrac{1}{\sqrt{3}(5\sqrt{3}-2\sqrt{2}\sqrt{3})}\\\\\\x=\dfrac{1}{(5.3-2.3\sqrt{2})}\\\\\\x=\dfrac{1}{15-6\sqrt{2}}\\\\\\x=\dfrac{1}{15-6\sqrt{2}}.\dfrac{15+6\sqrt{2}}{15+6\sqrt{2}}\\\\\\x=\dfrac{15+6\sqrt{2}}{225-72}\\\\\\x=\dfrac{15+6\sqrt{2}}{153}\\\\\\x=\dfrac{5+2\sqrt{2}}{51}$