Prove that if (x+1)² = x² + 2x, then (x+1)³ = π?

Answer 1

Suppose (x+1)² = x² + 2x. Then x² + 2x + 1 = x² + 2x, thus 0 = 1. Multiplying both sides by π - (x+1)³, we see that 0 = π - (x+1)³, thus (x+1)³ = π. Q.E.D.

Or more simply, we could simply observe that since the antecedent is never true, the conditional is vacuously true.

Answer 2

Pascal's answer is right. Another way to say it is: Suppose p and q are statements and p is false. Then the statement "p implies q" must be true. Here is the proof:

If "p implies q" is not true, then it must be the case
that p is true and q is false. But p is not true. Therefore
"p implies q" must be true after all.

Now, replace p by your first (false) equation and q by your second (false) equation.

Answer 3

(x+1)² = x² + 2x

therefore,

(x+1)³ = π

Answer 4

That is impossible, becuase (x+1)² never equals x²+2x