x^2 - y^2Math brain teasers require computations to solve.
Lester is very intent on finding a formula to calculate the difference between two squares but doesn't have any squared terms in it.
Eg: If x and y are two numbers with y>x then he wants to find a formula to calculate (y^2)-(x^2) which does not contain any x^2 or y^2 terms in it.
He finds that there are two cases:
a) when x and y are consecutive.
b) when x and y are not consecutive.
Can you help him find the formula?
HintTake some consecutive and nonconsecutive examples and try for yourself.
Answera) when x and y are consecutive, the difference between their squares is given by :
difference = x + y.
b) when x and y are not consecutive, the difference between their squares is given by :
difference = x + y + 2 * (sum of numbers between x and y)
You should note that part (a) is just a simplified version of (b), in which there are no numbers between x and y.
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