Problem #PRU-100261

Problems Algebra

Problem

Having had experience with some faulty proofs above, can you now answer the following questions

(a) From the equality \((a-b)^2=(m-n)^2\) may one draw the conclusion that \(a-b=m-n\)?

(b) For what value of \(x\) do the following expressions lose their meaning?

(1) \(\frac{x^3-1}{x-1}\), (2) \(\frac{1}{x^2-1}\), (3) \(\frac{x+1}{1-2^x}\).

(c) If \(a>b\), can one conclude that \(ac>bc\) for any number \(c\)?