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Для решения уравнения воспользуемся методом введения новых переменных. обозначим ∛(х+24)=а, √(12-х)=в, по условию а+в=6.
а³+в²=х+24+12-х=36
Приходим к системе уравнений а³+в²=36
а+в=6
из второго уравнения в=6-а, подставим его в первое, получим
а³+(6-а)²-36=0; а³+36-12а+а²-36=0; а³+а²-12а=0
а*(а²+а-12)=0
а₁=0; по теореме, обратной теореме Виета а₂=-4, а₃=3
Возвратимся к старой переменной х.
х+24=0, отсюда х= -24; х+24=(-4)³, откуда х=-64-24=-88,х+24=3³, отсюда х=27-24=3