Question

Rezolvati ecuatia:(x+2)^2-(x-3)^2=25
Aratati ca:(x-1)(x^2-1)-4(x+1)=(x+1)^2(x-3)

Answer 1

       
[tex] (x+2)^{2} - (x-3)^{2}=25 \\ x^{2}+4x+4-( x^{2} -6x+9)=25 \\ x^{2}+4x+4- x^{2} +6x-9=25 \\ 10x -5=25 \\ 10x = 25-5 \\ 10x=20 \\ x= \frac{20}{10}=\boxed{2} [/tex]


$(x-1)( x^{2} -1)-4(x+1) = \\ = x^{3} - x^{2} -x+1-4x-4= \\ = x^{3} - x^{2} -5x-3= \\=x^{3} + x^{2} - 2x^{2} -2x -3x-3= \\ =x^{2}(x + 1) - 2x(x + 1) -3(x + 1)= \\ =(x+1)(x^{2}- 2x-3)= \\=(x+1)(x^{2}+x- 3x-3)= \\=(x+1)(x(x+1)- 3(x+1))= \\ =(x+1)(x+1)(x- 3)= \\ =(x+1)^{2}(x- 3) \\ cctd$