3 = 0 can you please check what's wrong with this false proof?

Science & Mathematics by Anonymous 2018-06-16 15:02:44

Social Science

2 answers

x² + x + 1 = 0 Since x ≠ 0, we can divide both sides by x x + 1 + 1/x = 0 Subtituting x + 1 = - x², - x² + 1/x = 0 1/x = x² 1 = x³ ∴ x = 1 Substituting x = 1 into the original equation, (1)² + 1 + 1 = 0 3 = 0

Anonymous

There is no solution, not even using the complex plane.
Anonymous

The error is that "x^2+x+1=0" is assumed valid for real x. x=1 is not the root! x^3-1=(x-1)(x^2+x+1)=0 The real solution is x=1, but x=1 is not suitable for x^2+x+1=0 In fact, if x^2+x+1=0, then x=[-1+/-sqr(3)i]/2, not real.