Prove that the only solution of |x|+(y-1)²=0 is x=0 and y=1.

Question

Our math professor gave us a problem (as stated in the title) but I don't know where to start and how to write proofs.

Answer 1

Notice that both terms in the sum must be >= 0, so to sum to 0 they must both be 0 |x| = 0 only when x = 0 and (anything)^2 = 0 only when the term is 0 so y - 1 =0 or y = 1.

 

Both of these must happen at the same time so the only solution is x = 0 and y = 1.

 

The label Linear Algebra is incorrect. This is definitely NOT a Linear Algebra problem.