Question

[Gia Hân Nguyễn]

1) tìm x biết : 

a) -24 + 3 (x - 4) =111

b) ( 2x - 4) (3x + 63) = 0

c) |x - 7 | - 4 = (-2)⁴ 

d) ( x- 1) ² = 144

e) ( x + 7) ³ = -8 

2) tìm n \(\in\)N biết : 

a) 3n + 12 \(⋮\)n - 3 

b) n + 9 \(⋮\)n - 1 

Answer 1

[BLACK CAT]

 1)

a)-24+3(x-4)=111

           3(x-4)=111-(-24)

           3(x-4)=111+24

           3(x-4)=135

                x-4=135:3

                x-4=45

                 x  =45+4

                 x  =49

b)(2x-4)(3x+63)=0

\(\Rightarrow\)\(\orbr{\begin{cases}2x-4=0\\3x+63=0\end{cases}}\)\(\Rightarrow\)\(\orbr{\begin{cases}x=2\\x=-21\end{cases}}\)

Vậy x\(\in\){2;-21}

c)|x-7|-4=(-2)⁴

   |x-7|    =(-2)⁴+4

   |x-7|    =16+4

   |x-7|    =20

\(\Rightarrow\)\(\orbr{\begin{cases}x-7=7\\x-7=-7\end{cases}}\)\(\Rightarrow\)\(\orbr{\begin{cases}x=14\\x=0\end{cases}}\)

Vậy x\(\in\){14;0}

d)(x-1)²=144

    (x-1)²=12²

\(\Rightarrow\)x-1=12

          x  =12+1

          x  =13

e)(x+7)³=-8

   (x+7)³=(-2)³

\(\Rightarrow\)x+7=-2

         x     =-2-7

         x     =-9

2)

a)Ta có:

\(3n+12⋮n-3\)

\(\Rightarrow3n-9+21⋮n-3\)

\(\Rightarrow3\left(n-3\right)+21⋮n-3\)

\(\Rightarrow21⋮n-3\)

\(\Rightarrow n-3\inƯ\left(21\right)\)

\(\Rightarrow n-3\in\left\{1;3;7;21\right\}\)

Ta có bảng sau:

n-3	1	3	7	21
n	4	6	10	24

Vậy\(n\in\left\{4;6;10;24\right\}\)

b)Ta có:

\(n+9⋮n-1\)

\(\Rightarrow n-1+10⋮n-1\)

\(\Rightarrow10⋮n-1\)

\(\Rightarrow\)\(n-1\inƯ\left(10\right)\)

\(\Rightarrow n-1\in\left\{1;2;5;10\right\}\)

Ta có bảng sau:

n-1	1	2	5	10
n	2	3	6	11

Vậy \(n\in\left\{2;3;6;11\right\}\)