Question

rezolvati in R ecuatia$x*|x| + \frac{ x ^{3}+1 _}{x+1} - x^{0} =0$

Answer 1

lxl+[(x+1)(x^2-x+1)]/(x+1) -1=0
lxl+x^2-x+1-1=0
x^2 +lxl-x=0
l)x>=0
x^2+x-x=0
x^2=0
x=0
ll)x<0
x^2-x-x=0
x^2-2x=0
x(x-2)=0
x=0 sau x=2, dar x<0, ca in acest caz nu avem solutii.

Solutia rezultata este x=0 (in primul caz)

Answer 2

Folosim formula de calculm prescurat 9care NU intra in materiade gimnaziu si nici la Ev nationale)
x³+1=(x+1) (x²-x+1)
relatia devine
|x| +x²-x+1-1=0
|x| +x²-x=0
pt x≥0
x+x²-x=0
x²=0
 x=0∈D

pt x<0
-x+x²-x=0
x²-2x=0
x(x-2)=0

x=0 ∉D
x=2∉D

deci singura solutie x=0, care verifica
1-1=0