1,a)(-4)/9.7/9+17/9.(-1)/5-4/5.10/9
b)34/7.13+51/13.22+85/22.37+68/37.49
2,1) tìm x biết:
a)(7x-11)³=2⁵.5²+200
b) x+19/2019+x+18/2018+x+17/2017+…+x+1/2001=19
2) tìm các cặp số nguyên(x;y) thoả mãn:xy-2y+x-3=0
3) tìm n€Z để biểu thức A=3n-2/n+1 là phân số tối giản
37/7 . 13 + 51/13 . 22 + 85/22 . 37 + 68/37 . 49
= 17/3 . [1/7 – 1/13 + 1/13 – 1/22 + 1/22 – 1/37 + 1/37 – 1/49]
= 17/3 . [1/7 + (- 1/13 + 1/13 – 1/22 + 1/22 – 1/37 + 1/37) – 1/49]
= 17/3 . [1/7 – 1/49]
= 17/3 . 6/49
= 34/49
(7x−11)3=25.52+200
(7x−11)3=32.25+200
(7x−11)3=800+200=1000
(7x−11)3=1037
7x−11=10
7x=21
x=21:7
x=3.
3n+2⋮d3n+3⋮d{3n+2⋮d3n+3⋮d
⇒⇒ {3n+2⋮dn+1⋮d{3n+2⋮dn+1⋮d
⇒1⋮d⇒1⋮d
⇒d∈Ư(1)={±1}⇒d∈Ư(1)={±1}
⇒ƯCLN(3n+2;n+1)=±1⇒ƯCLN(3n+2;n+1)=±1
⇒A=⇒A= 3n+2n+13n+2n+1 là phân số tối giản
Bài 1
b,37/7 . 13 + 51/13 . 22 + 85/22 . 37 + 68/37 . 49
= 17/3 . [1/7 – 1/13 + 1/13 – 1/22 + 1/22 – 1/37 + 1/37 – 1/49]
= 17/3 . [1/7 + (- 1/13 + 1/13 – 1/22 + 1/22 – 1/37 + 1/37) – 1/49]
= 17/3 . [1/7 – 1/49]
= 17/3 . 6/49
= 34/49
Bài 2
a,(7x−11)3=25.52+200
(7x−11)3=32.25+200
(7x−11)3=800+200=1000
(7x−11)3=1037
7x−11=10
7x=21
x=21:7
x=3.