Determine,with a proof,whether each of the following equations is an identity.
(x+2)^2-(x-2)^2=8x
比式我thx!
I know that this equations is an identity
F.2math(20)
2010-10-15 1:26 am
回答 (3)
2010-10-15 1:40 am
✔ 最佳答案
(x+2)^2－(x－2)^2=(x^2+4x+4)－(x^2－4x+4)
=x^2+4x+4－x^2+4x－4
=8x
2010-10-15 2:14 am
A faster way to solve Q1:
_______________
LHS
(x+2)^2-(x-2)^2
(x+2-x+2)(x+2+x-2)
4(2x)
8x
RHS
it is an identity
_______________
LHS
(x+2)^2-(x-2)^2
(x+2-x+2)(x+2+x-2)
4(2x)
8x
RHS
it is an identity
2010-10-15 2:03 am
L.H.S=(x+2)^2-(x-2)^2
=[x^2+2(2x)+2^2]-[x^2-2(2x)+2^2]
=(x^2+4x+4)-(x^2-4x+4)
=x^2+4x+4-x^2+4x-4
=x^2-x^2+4x+4x+4-4
=8x
R.H.S=8x
Because L.H.S=R.H.S
So it is an identity.
=[x^2+2(2x)+2^2]-[x^2-2(2x)+2^2]
=(x^2+4x+4)-(x^2-4x+4)
=x^2+4x+4-x^2+4x-4
=x^2-x^2+4x+4x+4-4
=8x
R.H.S=8x
Because L.H.S=R.H.S
So it is an identity.
收錄日期: 2021-04-13 17:34:55
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