Bonsoir, j'arrive pas : résoudre X^2+ (X-1)^2 + (X+3)^2 = (X+3)^2+ (X+1)^2 Merci d'avance !

bonsoir

X^2+ (X-1)^2 + (X+3)^2 = (X+3)^2+ (X+1)^2
x² +x²-2x+1 +x²+6x+9 = x²-6x+9+x²+2x+1
3x²+4x+10 = 2x²-4x+10
3x²+4x+10-2x²+4x-10 =0
x²+8x = 0
x(x+8) =0

x =0                       x+8 =0
                               x = -8

X²+ (X-1)²+ (X+3)²= (X+3)²+ (X+1)² .
x²+(x-1)²+(x+3)²-(x+3)²-(x+1)=0
x²+(x-1)²-(x+1)²=0
x²+(x-1-(x+1)) (x-1+x+1)=0
x²+(-2) (2x)=0
x²-4x=0
x(x-4)=0
donc x=0 ou x=4