Question

Sabendo que R = √24 + √54 e J = √32 - √98, qual o valor de √3.R/3J?

a) 5/4
b) 1/2
c) -2/3
d) -5/3​

Answer 1

Resposta:

Alternativa (d)

Explicação passo a passo:

$\sqrt{24} =2\sqrt{6} \\\sqrt{54} = 3\sqrt{6}\\ \sqrt{32} =4\sqrt{2} \\\sqrt{98} = 7\sqrt{2} \\\\R=2\sqrt{6} +3\sqrt{6} \\R=5\sqrt{6} \\\\J=4\sqrt{2} -7\sqrt{2} \\J=-3\sqrt{2} \\\\\\\frac{\sqrt{3} .R}{3J} = \frac{\sqrt{3}.5\sqrt{6} }{3.(-3\sqrt{2}) } \\\\\frac{\sqrt{3} .R}{3J} =\frac{5\sqrt{18} }{-9\sqrt{2} }$

Fatorando √18 = 3√2

$\frac{\sqrt{3} .R}{3J} =\frac{5 * 3\sqrt{2} }{-9\sqrt{2} } \\\\\frac{\sqrt{3} .R}{3J} =\frac{15\sqrt{2} }{-9\sqrt{2} }$

Cancela a √2

$\frac{\sqrt{3}.R }{3J}= \frac{15 }{-9} }\\\\\frac{\sqrt{3}.R }{3J}=\frac{-5}{3}$