Đáp án:
Giải thích các bước giải:
a) [ 1/2 + 16/30 ] - [ 1 + |-1/30| ] b) 3/2 - 2/3 - 2/3 x 5/4
= 1/2 + 8/15 - 1 - 1/30 = 3/2 - 1 x 2/3 - 2/3 x 5/4
= [ 1/2 - 1 ] + [ 8/15 - 1/30 ] = 3/2 - 2/3 x [ 1+ 5/4 ]
= -1/2 + 1/2 = 3/2 - 2/3 x 9/4
= 0 = 1 x 3/2 - 2/3 x 3/2 x 3/2
= 3/2 x [ 1 - 1 ]
= 3/2 x 0
= 0
c) [ 2/9 : 5/3 + 1/3 : 5/3 ]^2 - [ 1/3 - 5/8 ]
= {[ 2/9 + 1/3 ] : 5/3 }^2 - [ 1/3 - 5/8 ]
= [ 5/9 : 5/3 ]^2 - [ 1/3 - 5/8 ]
= 1/9 - [-7/24]
= 29/72
Bài 2: Tìm x, biết
a) -5/6 - x = 7/12 + -1/3 b) 2 . [ x - 1/3 ] = [1/3]^2 + 5/9
-5/6 - x = 1/4 2 . [ x - 1/3 ] = 2/3
x = -5/6 - 1/4 x - 1/3 = 2/3 : 2
x = -13/12 x - 1/3 = 1/3
Vậy x = -13/12 x = 1/3 : 1/3
x = 1
Vậy x = 1
c) | 2x - 3/4 | - 3/8 = 1/8
| 2x - 3/4 | = 1/8 + 3/8
| 2x - 3/4 | = 1/2
=> 2x - 3/4 = +- 1/2
Nếu 2x - 3/4 = 1/2 Nếu 2x - 3/4 = -1/2
=> 2x = 5/4 => 2x = 1/4
x = 5/8 x = 1/4 : 2
x = 1/8
Vậy x = 5/8 hoặc 1/8
Bài 3: Tính tổng A = 3/1x3 + 3/3x5 + 3/5x7 +...+ 3/49x51
3/1x3 + 3/3x5 + 3/5x7 +...+ 3/49x51
= 3/2 x [ 2/1x3 + 2/3x5 + 2/5x7 +...+ 2/49x51
= 3/2 x [ 1 - 1/51 ]
= 3/2 x 50/51
= 25/17
