Question

$\sqrt[3]{5x+7}$-$\sqrt[3]{5x-12}$=1

Answer 1

prin substitutie
$\sqrt[3]{5x+7}=a \\ \sqrt[3]{5x-12}=b$
obtinem sistemul
$\left \{ {{a-b=1} \atop {a^3}-b^3=19 \right.$
$\left \{ {{a=b+1} \atop {b^3+3b^2+3b+1-b^3=19}} \right.$
$\left \{ {{b=a+1} \atop {3b^2+3b-18=0}} \right.$
$\left \{ {{a=b+1} \atop {b^2+b-6=0}} \right.$
$\left \{ {{a=3} \atop {b=2}} \right. sau \left \{ {{a=-2} \atop {b=-3}} \right.$