domingo, 15 de enero de 2017

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 

No hay comentarios:

Publicar un comentario en la entrada