Question

When you subtract one square number from another the answer is 8, what are the two square numbers

Answer 1

We want to find the integer solutions to x2−y2=8. We use ‘difference of two squares’ to factorise the left hand side, which gives

(x+y)(x−y)=8

Now the two brackets have to be integers, and clearly they divide into 8. Thus the only options are 1,2,4,8. Notice that the brackets are either both even or both odd. This eliminates (1,8) as a solution, meaning the brackets have value (2,4). Solving gives x=3 and y=1 (the negative solutions are valid but the question only asks about the square numbers themselves so this is irrelevant). So the square numbers are 9 and 1.

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Answer 2

Answer:

We wants to find the integer solution to x^2 - y^2 = 8, we use the difference of two square to factorise the left hand side which gives:

(x+y)(x-y) = 8

Now, the two bracket have to be integers and clearly they divide into 8. Thus, the only options are 1,2,4,8.Notice that are either both even or both odd. This eliminates ( 1,8 ) as the solution , meaning the bracket have value ( 2,4) . Solving gives x= 3 and y= 1 ( the negative solution are valid but the question asks about the square number themselves this is irrelevant).

So, the square numbers are 9 and 1.

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