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# Identities

(a) Prove that ( x - 2 ) ( x + 1 ) = x^ 2 - x - 2 is an identity

(b) By using th result of (a), prove that ( y - 3 ) y = ( y - 1 )^ 2 - y - 1

我唔係好明(b)想我地做D咩,可唔可以同我解釋一下?

*thx*

To larissachia:唔係呀,本書話有關係架

### 2 Answers

- 1 decade agoFavorite Answer
a) Prove that

( x - 2 ) ( x + 1 )

is an identity

L.H.S.

( x - 2 ) ( x + 1 )

=x(x-2)+ 1(x-2)

= x^2- 2x+ x- 2

= x^2- x- 2

=R.H.S.

L.H.S.=R.H.S.

( x - 2 ) ( x + 1 )=x^ 2 - x - 2 is an identity

b) prove that

( y - 3 ) y = ( y - 1 )^ 2 - y - 1

is an identity

R.H.S.

=y^2- 2y+ 1^2- y- 1

=y^2- 3y

L.H.S.

=( y - 3 ) y

=y^2- 3y

=R.H.S.

L.H.S.=R.H.S.

( y - 3 ) y = ( y - 1 )^ 2 - y - 1is an identity

我想a同b應該無乜關系

但係b你要應用到

(a-b)^2 = a^2- 2ab +b^2

Source(s): me - 1 decade ago
(a) L.H.S = (x-2)(x+1)

=x^2-2x+x-2

=x^2-x-2

=R.H.S

therefore, (x-2)(x+1)=x^2-x-2 is an identity

(b) By (a), (x-2)(x+1)=x^2-x-2

substituting x=y-1into the above identity,

(y-1-2)(y-1+1)=(y-1)^2-(y-1)-2

(y-3)y=(y-1)^2-y-1

2007-12-01 21:31:16 補充：

Actually, (b) wants you to use the method of substitution after finding the results of (a).