? asked in 科學及數學數學 · 1 decade ago

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*

Update:

To larissachia:唔係呀,本書話有關係架

2 Answers

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  • 1 decade ago
    Favorite 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).

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