Question

Express 22 as the difference the two squares... please PLASE help me guys... please​

Answer 1

Answer:

You can express 22 of the 30 numbers as a difference of two perfect squares. A pattern occuring throughout these solutions is that all odd numbers can be represented by a difference of two perfect squares, as well as all numbers resulting in an integer when divided by four.

Joshua from St John's School used algebra to show how odd numbers and multiples of four could be made:

You can make every odd number by taking consecutive squares.

$(n+1)^2 - n^2 = 2n+1$, every odd number can be written in the form $2n+1$.(n+1)2−n2=2n+1, every odd number can be written in the form 2n+1.

Similarly, you can make every multiple of 4 by taking squares with a difference of 2.

All other numbers you can't make:

$(n+x)^2 - n^2 = x^2 + 2nx = x(x+2n)$(n+x)2−n2=x2+2nx=x(x+2n)

If $x$ is odd then $x^2$ is also odd and $2nx$ is even. An odd plus an even is odd.x is odd then x2 is also odd and 2nx is even. An odd plus an even is odd.

If $x$ is even then $x^2$ is a multiple

Step-by-step explanation:

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