Numbers and Functions (10 marks) Urgent!!!!!!!!!

billyhorsewater2620888

2007-09-28 3:20 am

1(a) Simplify (2x+1)^2 + (2x-1)^2
(b) Hence prove that the sum of the squares of any two consecutive odd numbers is an even number.

回答 (1)

Tom

2007-09-28 3:26 am

✔ 最佳答案

1a)
(2x+1)^2 + (2x-1)^2
=4x^2+4x+1+4x^2-4x+1
=8x^2+2

1b)
We know that 2x+1 and 2x-1 are add numbers no matter x is an odd or even number.
From (1a),
(2x+1)^2 + (2x-1)^2
=8x^2+2
=2(x^2+1)
So, the sum of the squares of any two consecutive odd numbers is an even number because the sum can be divide by 2.

2007-09-27 19:27:39 補充：
Sorry, I make a mistake, just skip the statement:We know that 2x 1 and 2x-1 are add numbers no matter x is an odd or even number.

2007-09-27 19:28:26 補充：
If you still don't understand, please contact me.

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