Các bạn nào mà làm bài này thì ghi chữ ❝ trả lời ❞ và các cố gắng ghi từng bước ra nhé !
Câu 1)
1) \(\dfrac{11}{24}-\dfrac{5}{41}+\dfrac{13}{24}+0,5-\dfrac{36}{41}\)=
2)\(12\div\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2\)=
3)\(\left(1+\dfrac{2}{3}-\dfrac{1}{4}\right)\left(0,8-\dfrac{3}{4}\right)^2\)=
4)\(16\dfrac{2}{7}\div\left(\dfrac{-3}{5}\right)+28\dfrac{2}{7}\div\dfrac{3}{5}\)
5)\(\left(2^2\div\dfrac{4}{3}-\dfrac{1}{2}\right)\times\dfrac{6}{5}-17\)
6)\(\left(\dfrac{1}{3}\right)^{50}\times-9^{25}-\dfrac{2}{3}\div4\)
7)\(10\times\sqrt{0,01}\times\sqrt{\dfrac{16}{9}}+3\sqrt{49}-\dfrac{1}{6}\sqrt{4}\)
Bài 2) Tìm x biết
1)\(\dfrac{x}{12}-\dfrac{5}{6}=\dfrac{1}{12}\)
2)\(\dfrac{2}{3}-1\dfrac{4}{15}x=\dfrac{-3}{5}\)
3)\(\dfrac{\left(-3\right)^x}{81}=-27\)
4)\(\left|x+0,237\right|=0\)
5)\(\left(x-1\right)^2=25\)
6)\(\left|2x-1\right|=5\)
7)\(\left(x-1\right)^3=\dfrac{-8}{27}\)
8)\(1\dfrac{2}{3}\div\dfrac{x}{4}=6\div0,3\)
9)\(2\dfrac{2}{3}\div x=1\dfrac{7}{9}\div2\dfrac{2}{3}\)
Bài 3)Tìm các số x,y,z biết
1) \(\dfrac{x}{7}=\dfrac{y}{3}\) và \(x-24=y\)
2) \(\dfrac{x}{5}=\dfrac{y}{7}=\dfrac{z}{2}\) và x - y = 48
3) \(\dfrac{x-1}{2005}=\dfrac{3-y}{2006}\) và x - y = 4009
4) \(\dfrac{x}{2}=\dfrac{y}{3};=\) và x - y - z = 28
5) \(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{7}\) và 2x +3y -z = -14
6) 3x = y ; 5y = 4z và 6x +7y +8z =456
a, \(A=\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+...+\dfrac{5^2}{26.31}\)
\(A=5.\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{26.31}\right)\)
\(A=5.\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\)
(do \(\dfrac{n}{a\left(a+n\right)}=\dfrac{1}{a}-\dfrac{1}{a+n}\) với \(a\in N\)*)
\(A=5.\left(1-\dfrac{1}{31}\right)=5.\dfrac{30}{31}=\dfrac{150}{31}\)
b, \(B=\dfrac{6}{15.18}+\dfrac{6}{18.21}+...+\dfrac{6}{87.90}\)
\(B=2\left(\dfrac{3}{15.18}+\dfrac{3}{18.21}+...+\dfrac{13}{87.90}\right)\)
\(B=2\left(\dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+...+\dfrac{1}{87}-\dfrac{1}{90}\right)\)
(do \(\dfrac{n}{a\left(a+n\right)}=\dfrac{1}{a}-\dfrac{1}{a+n}\) với \(a\in N\)*)
\(B=2\left(\dfrac{1}{15}-\dfrac{1}{90}\right)=2.\dfrac{1}{18}=\dfrac{1}{9}\)
c, \(C=\dfrac{3^2}{8.11}+\dfrac{3^2}{11.14}+...+\dfrac{3^2}{197.200}\)
\(C=3\left(\dfrac{3}{8.11}+\dfrac{3}{11.14}+...+\dfrac{3}{197.200}\right)\)
\(C=3\left(\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+...+\dfrac{1}{197}-\dfrac{1}{200}\right)\)
(do \(\dfrac{n}{a\left(a+n\right)}=\dfrac{1}{a}-\dfrac{1}{a+n}\) với \(a\in N\)*)
\(C=3\left(\dfrac{1}{8}-\dfrac{1}{200}\right)=3.\dfrac{3}{35}=\dfrac{9}{35}\)
Chúc bạn học tốt!!!
Cảm ơn Đoàn Đức Hiếu nhiều!