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08 Nov 2019, 12:56
Kudos
Bookmarks
Hi there,
I need help trying to solve the following:
If X and Y are two positive integers such that the product of their sum and difference is 40, what is the value of X-Y?
If X is the difference between the squares of two non-consecutive integers then is X prime?
I need help trying to solve the following:
If X and Y are two positive integers such that the product of their sum and difference is 40, what is the value of X-Y?
If X is the difference between the squares of two non-consecutive integers then is X prime?
11 Nov 2019, 13:13
Kudos
Bookmarks
kevinkhan
Hi there,
I need help trying to solve the following:
I need help trying to solve the following:
If you're familiar with the term 'difference of squares', as written in the name of this thread, you already know most of what you need to solve these!
Quote:
If X and Y are two positive integers such that the product of their sum and difference is 40, what is the value of X-Y?
The product of their sum and difference is (x + y)(x - y), which equals the difference of squares, or \(x^2 - y^2\). In other words, \(x^2 - y^2=40\).
From here, guess and check to find two positive integers whose squares are 40 apart from each other. I actually found two different pairs.
Quote:
If X is the difference between the squares of two non-consecutive integers then is X prime?
If x is the difference of squares, then you can rewrite x as \(a^2 - b^2\), which can be written as \((a-b)(a+b)\). In that case, is x prime?
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