1.Tính: (2x-5)^3 2. Cho a+b+c = 0. C/m a^3 + b^3 + c^3 = 3abc

Question

1.Tính: (2x-5)^3
2. Cho a+b+c = 0. C/m a^3 + b^3 + c^3 = 3abc

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Iris 3 tháng 2021-09-09T10:48:12+00:00 2 Answers 6 views 0

Answers ( )

    0
    2021-09-09T10:49:46+00:00

    Bài giải:

    Câu 1:

    (2x-5)³

    = 2x³ -125

    Câu 2:

    a+b+c=0

    ⇔a+b=-c

    ⇔(a+b)³=-c³

    ⇔a³+b³+3ab(a+b)=-c³

    ⇔a³+b³-3abc=-c³(Vì a+b=-c)

    ⇔a³+b³+c³=3abc

    Goodluck^.^

    0
    2021-09-09T10:49:50+00:00

    1, (2x-5)  mu 3

    = 2x mu 3 -125

    2, Ta có

    a+b+c = 0

    => a+b = -c

    => $(a+b)^{3}$ = $-c^{3}$ 

    => $a^{3}$ + $b^{3}$ + $c^{3}$ = $-3a^{2}b$ – $3ab^{2}$

    => $a^{3}$ + $b^{3}$ + $c^{3}$ = -3a (a+b)

    Vì a+b= -c

    => (đpcm)

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