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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: $5^{6}$ + $5^{5}$ + $5^{4}$ + 2.$5^{3}$ + $5^{2}$ + 5 + 1 chia hết cho 126

Toán Lớp 8: $5^{6}$ + $5^{5}$ + $5^{4}$ + 2.$5^{3}$ + $5^{2}$ + 5 + 1 chia hết cho 126

Comments ( 2 )

  1. 5^{6} + 5^{5} + 5^{4} + 2.5^{3} + 5 + 1
    =5^{6} + 5^{3} + 5^{5} + 5^{2} + 5^{4} + 5 + 5^{3} + 1
    =5^{3}(5^{3} + 1) + 5^{2}(5^{3} + 1) + 5(5^{3} + 1) + 5^{3} + 1
    =(5^{3} + 1)(5^{3} + 5^{2} + 5 +1)
    =126(5^{3} + 5^{2} + 5 +1) \vdots 126
    =>126(5^{3} + 5^{2} + 5 +1) \vdots 126 (đpcm)

  2. Giải đáp+Lời giải và giải thích chi tiết:
    5^6 + 5^5 + 5^4 + 2 . 5^3 + 5^2 + 5 + 1
    = 5^6 + 5^5 + 5^4 + 5^3 + 5^3 + 5^2 + 5 + 1
    = 5^5(5 + 1) + 5^3(5 + 1) + 5^2(5 + 1) + (5 + 1)
    = 5^5 . 6 + 5^3 . 6 + 5^2 . 6 + 6
    = 6 . (5^5 + 5^3 + 5^2 + 1)
    = 6 . [5^3(5^2 + 1)(5^2 + 1)]
    = 6 . [(5^2 + 1)(5^3 + 1)]
    = 6 . (5^2 + 1) . (125 + 1)
    = 126 . 6 . (5^2 + 1)
    Mà 126 . 6 . (5^2 + 1) \vdots 126
    ⇒ 5^6 + 5^5 + 5^4 + 2 . 5^3 + 5^2 + 5 + 1 \vdots 126

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222-9+11+12:2*14+14 = ? ( )