Question

$sqrt[3]{ frac{5x + 2}{x + 3} } + sqrt[3]{ frac{x + 3}{5x + 2} } = frac{13}{6}$

Answer 1

∛[(5x+2)/(x+3)]=t
t+1/t=13/6
6t²-13t+6=0
D=169-144=25
t1=(13-5)/12=2/3⇒∛[(5x+2)/(x+3)]=2/3
(5x+2)/(x+3)=8/27
135x+54=8x+24
135x-8x=24-50
127x=-26
x=-26/127
t2=(13+5)/12=3/2⇒∛[(5x+2)/(x+3)]=3/2
(5x+2)/(x+3)=27/8
40x+16=27x+81
40x-27x=81-16
13x=65
x=5