1237. A radical equation with cube roots

    This equation was solved by a pupil of mine... Pepe Chapuzas again!

³√(1729 − x)  =  19 − ³√x

cubing...

1729 − x  =  19³ − 3 · 19² · ³√x + 3 · 19 · ³√x² − x

57 · ³√x² − 1083 · ³√x + 5130  =  0

quadratic formula...

³√x  =  (1083 ± √3249) / 114 =  (1083 ± 57) / 114
x  =  (1083 ± 57)³ / 114³
x₁  =  1000
x₂  =  729

 checking...

³√(1729 − 1000) + ³√1000  =  ³√729 + ³√1000  =  9 + 10  =  19
³√(1729 − 729) + ³√729  =  ³√1000 + ³√729  =  10 + 9  =  19