Question

Найдите a^3+b^3+c^3/abc , если a/2=b/3=c/4
a)1/8
b)33/8
c)2
d)1/2
e)3/8​

Answer 1

$\frac{a}{2}=\frac{b}{3}\ /\cdot2\\a=\frac{2}{3}b\\\\\frac{b}{3}=\frac{c}{4}\ /\cdot4\\c=\frac{4}{3}b\\\\\frac{a^3+b^3+c^3}{abc}=\frac{(\frac{2}{3}b)^3+b^3+(\frac{4}{3}b)^3}{\frac{2}{3}b\cdot b\cdot\frac{4}{3}b}=\frac{\frac{8}{27}b^3+b^3+\frac{64}{27}b^3}{\frac{8}{9}b^3}=\frac{\frac{99}{27}b^3}{\frac{8}{9}b^3}=\frac{33}{8}$

Ответ: b) 33/8