Bài 1 a, Tìm số tự nhiên x , biết ( 3 . x – $15)^{7}$ = 0 $4^{2.x-6}$ = 1 {[2.x + 14 ) :$2^{2}$ – 3 ] : 2 } – 1 =0 10 – {[ x : 3 + 17 ) :10 + 3 . $

Question

Bài 1
a, Tìm số tự nhiên x , biết
( 3 . x – $15)^{7}$ = 0
$4^{2.x-6}$ = 1
{[2.x + 14 ) :$2^{2}$ – 3 ] : 2 } – 1 =0
10 – {[ x : 3 + 17 ) :10 + 3 . $2^{4}$ ] : 10 } = 5
b,chứng minh rằng
Tổng A = $5^{2003}$ + $5^{2002}$ + $5^{2001}$ chia hết cho 31
Tổng B = $3^{3}$ + $3^{2}$ + $3^{3}$ +$3^{4}$ + … +$2^{2010}$ chia hết cho 4
CÁC BN LM HẾT CHO MIK NHA

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Vivian 3 tuần 2021-08-20T05:24:02+00:00 2 Answers 2 views 0

Answers ( )

    0
    2021-08-20T05:25:08+00:00

    Đáp án:

    $\begin{array}{l}
    B1)\\
    a){\left( {3x – 15} \right)^7} = 0\\
     \Rightarrow 3x – 15 = 0\\
     \Rightarrow x = 5\\
    \text{Vậy}\,x = 5\\
    b){4^{2x – 6}} = 1\\
     \Rightarrow {4^{2x – 6}} = {4^0}\\
     \Rightarrow 2x – 6 = 0\\
     \Rightarrow x = 3\\
    \text{Vậy}\,x = 3\\
    c)\left\{ {\left[ {\left( {2x + 14} \right):{2^2} – 3} \right]:2} \right\} – 1 = 0\\
     \Rightarrow \left\{ {\left[ {\left( {2x + 14} \right):4 – 3} \right]:2} \right\} = 1\\
     \Rightarrow \left[ {\left( {x + 7} \right):2 – 3} \right] = 2\\
     \Rightarrow \left( {x + 7} \right):2 = 2 + 3 = 5\\
     \Rightarrow x + 7 = 5.2 = 10\\
     \Rightarrow x = 10 – 7 = 3\\
    \text{Vậy}\,x = 3\\
    d)10 – \left\{ {\left[ {\left( {x:3 + 17} \right):10 + {{3.2}^4}} \right]:10} \right\} = 5\\
     \Rightarrow \left[ {\left( {x:3 + 17} \right):10 + {{3.2}^4}} \right]:10 = 10 – 5 = 5\\
     \Rightarrow \left( {x:3 + 17} \right):10 + 3.16 = 5.10 = 50\\
     \Rightarrow \left( {x:3 + 17} \right):10 = 50 – 48 = 2\\
     \Rightarrow x:3 + 17 = 2.10 = 20\\
     \Rightarrow x:3 = 20 – 17 = 3\\
     \Rightarrow x = 3.3 = 9\\
    \text{Vậy}\,x = 9\\
    Bb)\\
    A = {5^{2003}} + {5^{2002}} + {5^{2001}}\\
     = {5^{2001}}\left( {{5^2} + 5 + 1} \right)\\
     = {5^{2001}}.\left( {25 + 5 + 1} \right)\\
     = {5^{2001}}.31 \vdots 31\\
    B = 3 + {3^2} + {3^3} + {3^4} + … + {3^{2010}}\\
     = 3.\left( {1 + 3} \right) + {3^3}.\left( {1 + 3} \right) + … + {3^{2009}}.\left( {1 + 3} \right)\\
     = 3.4 + {3^3}.4 + … + {3^{2009}}.4\\
     = \left( {3 + {3^3} + … + {3^{2009}}} \right).4 \vdots 4
    \end{array}$

    0
    2021-08-20T05:25:59+00:00

    Đáp án:

     

    Giải thích các bước giải:

    a) (3 . x – 15)⁷ = 0

    <=> 3 . x – 15 = 0

    <=> 3 . x = 15

    <=>      x = 5

        4^( 2x – 6) = 1

    <=> 2x – 6 = 0

    <=> 2x = 6

    <=>  x = 3

    {[( 2.x  + 14): 2² – 3] : 2}  – 1 = 0

    <=> [( 2x + 14) : 4 – 3] :2 = 1

    <=> ( 2x + 14) : 4 – 3 = 2

    <=> ( 2x + 14 ) : 4 = 5

    <=> 2x + 14 = 20

    <=> 2x = 6

    <=> x = 3

    10 – {[(x :3 + 17) :10 + 3.2⁴] :10} =5

    <=> [(x : 3 + 17) : 10 + 3.16] :10 = 5

    <=> ( x : 3 + 17) : 10 + 48 = 50

    <=> ( x : 3 + 17) : 10 = 2

    <=>  x : 3 + 17 = 20

    <=>  x : 3 =  3

    <=>  x     = 9

    b) A = 5²⁰⁰³ + 5²⁰⁰² + 5²⁰⁰¹ 

        A = 5²⁰⁰¹.( 5² + 5 + 1)

       A = 5²⁰⁰¹ . 31

    => A chia hết cho 31

    B = 3¹ + 3² + 3³ + 3⁴ +… +  3²⁰¹⁰

    B = ( 3¹ + 3²) + ( 3³ + 3⁴ ) +… + 

    ( 3²⁰⁰⁹ + 3²⁰¹⁰)

    B = 3.(1 + 3) + 3³.( 1 + 3) + … +

    3²⁰⁰⁹.( 1 + 3)

    B = 3.4 + 3³ . 4 + … + 3²⁰⁰⁹ . 4

    B = 4.( 3 + 3³ + … + 3²⁰⁰⁹)

    => B chia hết cho 4

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