Question

Sa se determine numerele intregi care verifica egalitatile:
a) |x(x-2) -(x-3)²|=3
b) |(2-x) (x+2)+(x+3)²|=5

Answer 1

a) |x(x-2) -(x-3)²|=3
|x²-2x -(x²-6x+9)|=3
|x²-2x -x²+6x-9|=3
|4x-9|=3
4x-9=3
x=12/4=3

b) |(2-x) (x+2)+(x+3)²|=5
|(2-x) (2+x)+(x²+6x+9)|=5
|4-x²+x²+6x+9|=5
|6x+13|=5
-(6x+13)=5
-6x-13x=5
-6x=18
x=-3