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

Toán Lớp 8: Hãy so sánh A và B A=4( $3^{2}$ +1)(3^4+1)(3^8+1)(3^16+1)(3^32+1) B=3^64-1

Tháng Tám 16, 2022 Toán học 2 Comments 0 views

Toán Lớp 8: Hãy so sánh A và B
A=4( $3^{2}$ +1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
B=3^64-1

Comments ( 2 )

  1. daolanhoa
    daolanhoa
    16 Tháng Tám, 2022 at 9:38 chiều
    Reply
    Giải đáp+Lời giải và giải thích chi tiết:
    Ta có:
    A=4(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
    =>2A=2.4(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
    =8.(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
    =(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
    =(3^4-1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
    =(3^8-1)(3^8+1)(3^16+1)(3^32+1)
    =(3^16-1)(3^16+1)(3^32+1)
    =(3^32-1)(3^32+1)
    =3^64-1
    =>A={3^64-1}/2
    Vì {3^64-1}/2<3^64-1
    hay 4(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)<3^64-1
    =>A<B
    Vậy A<B

  2. thanoanghha
    thanoanghha
    16 Tháng Tám, 2022 at 9:38 chiều
    Reply
    $\\$
    A=4(3^2 +1)(3^4+1)(3^8 +1)(3^{16}+1)(3^{32}+1)
    -> 2 A = 8 (3^2 +1)(3^4 +1)(3^8 +1)(3^{16}+1)(3^{32}+1)
    -> 2A = (3^2-1) (3^2 +1)(3^4 +1)(3^8 +1)(3^{16}+1)(3^{32}+1)
    ->2A = (3^4 – 1) (3^4 +1)(3^8 +1)(3^{16}+1)(3^{32}+1)
    ->2A=(3^8 – 1) (3^8 +1)(3^{16}+1)(3^{32}+1)
    ->2A=(3^{16} -1) (3^{16}+1)(3^{32}+1)
    ->2A=(3^{32-1})(3^{32}+1)
    -> 2A=3^{64}-1
    ->A = (3^{64}-1)/2
    Vì (3^{64}-1)/2 < 3^{64}-1
    ->A < B
    Vậy A<B

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

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