Question

Sa se rezolve ecuatia:​

Answer 1

Răspuns:

DVA   x≥0

Substitutie  √x=y   ,  y≥0

Ecuatia  devine

∛(y+3)+∛(13-y)=4

∛(y+3)=4-∛(13-y)

Ridici  la  cub

(y+3)=4-3*4²∛(13-y)+3*4∛(13-y)²-(13-y)

y+3=4³-48∛(13-y)+12∛(13-y)²-13+y

3=64-48∛(13-y)+12∛(13-y)²-13

0=51-3-48∛(13-y)+12√(13-y)²

12∛(13-y)²-48∛(13-y)²+48=0║12

∛(13-y)²-4∛(13-y)+4=0

∛(13-y)=t  substitutie

t²-4t+4=0

(t-2)²=0

t=2

∛(13-y)=2=>

13-y=2³

13-y=8

y=13-8

y=5=>

√x=5

x=5²

x=25

Explicație pas cu pas: