Brain Teasers
x^2 - y^2
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?
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?
Hint
Take some consecutive and nonconsecutive examples and try for yourself.Answer
a) 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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Comments
the way we leant it, the formula for finding the difference of 2 squares is (x+y)(x-y) ... am i missing out something?
You're right, moi.
I'd rather use (y+x)(y-x) than Lester's formula, particularly if the difference between x and y is large. You'd need another formula to calculate that sum!
I'd rather use (y+x)(y-x) than Lester's formula, particularly if the difference between x and y is large. You'd need another formula to calculate that sum!
Just_moi, you're just restating the question with your answer. If you multiply your answer out, you get x^2 - y^2. The question asks for ANOTHER way to express this, without using any x^2 or y^2 terms in it. Maybe the teaser could be explained a little more clearly, but I like the idea behind this one.
I know it's an old teaser but if anyone is still confused if you look at (y+x)(y-x) for consecutive numbers then (y-x)=1, so it simplifies to y+x.
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