You have a calculator whose multiplication button is broken. The only operations that work are addition (x+y), subtraction (x-y), and reciprocation (1/x).

Can you use this calculator to multiply two numbers?

We can calculate x^2/4 for any x by doing 1/(2+x) + 1/(2-x) which equals 4/(4-x^2). Reciprocating then gives 1-x^2/4. Subtracting 1 gives -x^2/4 and subtracting this from 0 gives x^2/4.

Now ab = (a+b)^2/4 - (a-b)^2/4 and this can therefore be computed by a calculator with enough levels of parenthesis, or if we have STO and RCL like my TI-30X SOLAR has.

Posted by Richard on 2005-01-21 00:15:12