Prove that the square of an odd number is always 1 more than a multiple of 4.
Input note: use 2n +1 as your odd number, and leave your answer in the form
4(...) +1
(4 marks)

Question

07-03-2021
Mathematics

Answered

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Prove that the square of an odd number is always 1 more than a multiple of 4.
Input note: use 2n +1 as your odd number, and leave your answer in the form
4(...) +1
(4 marks)

Sagot :

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birronbaronbasdnaym birronbaronbasdnaym · Answer 1 · 2021-03-07T08:14:45-05:00

Answer:

See explanation.

Step-by-step explanation:

If the odd number is 2n+1 note that n can be any number because any even number plus one will be odd. Let's start by squaring 2n+1 to get:

[tex]4n^2+4n+1[/tex]

Consider xy (x times y). xy is a multiple of both x and y because xy/x = y and xy/y = x. So it doesn't matter what n is it will be a multiple of 4. So now we know that 4n^2 and 4n are both multiples of 4. If we add them together, it will still be a multiple of 4. 2x + 4x = 6x and 6x is still divisible by x.

Now the plus 1 will always make it so it will be one more than a multiple of 4.

Prove that the square of an odd number is always 1 more than a multiple of 4. Input note: use 2n +1 as your odd number, and leave your answer in the form 4(...) +1 (4 marks)

Sagot :

Other Questions

Prove that the square of an odd number is always 1 more than a multiple of 4.
Input note: use 2n +1 as your odd number, and leave your answer in the form
4(...) +1
(4 marks)