1. Tìm a,b,c biết:
a) a/b = 8/5; b/c = 2/7 và a+b+c= 61
b) ab = 1/2; bc= 2/3; ac = 3/4
c) 3a=2b; 5b = 7c và 3a + 5c - 7b= 60
2. tìm các số nguyên n sao cho:
1) 5^n + 5^n+2 = 650
2) 32^-n .16^n = 1024
3) 3^-1 .3^n+ 5. 3^n-1 = 162
4) 125. 5\(\ge\)5^n\(\ge\)5 . 25
5) (n^54)^2 = n
6) 243\(\ge\)3^n\(\ge\)9.27
7) 2^n+3 . 2^n = 144
8)3<3^n\(\le\)234
9) 8. 16\(\ge\)2^n\(\ge\)4
10) 4^15. 9^15<2^n.3^n< 18^16. 2^16
11) 4^11. 25^11\(\le\)2^n. 5^n\(\le\)20^12. 5^12
12)\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\).\(\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}\)= 2^n
13) 9. 27^n= 3^5
14) (2^3 : 4) . 2^n= 4
15) 3^-2 . 3^4. 3^n = 3^7
16)2^-1. 2^n +4.2^n=9.2^5
Tìm x e Q, biết :
1. \(\left(1-2x\right)^4\) = 81
2. Giá trị tuyệt đối của 2,5 - x = 1,3
3. \(5^x\) + 5 x +2 = 650
4 . \(\dfrac{3}{8}\) + x - \(\left(-\dfrac{5}{6}\right)\)= \(1\dfrac{1}{3}\)
5.\(-\dfrac{3}{14}\) x + \(\dfrac{5}{7}\) = \(\dfrac{3}{4}\)
Tìm nghiệm của các đa thức sau:
a, \(\dfrac{5}{6}\)- | 2-x | =\(\dfrac{1}{3}\)
b, | x- \(\dfrac{2}{5}\) | + \(\dfrac{1}{2}\)= \(\dfrac{3}{4}\)
c, | 5-3x | + \(\dfrac{2}{3}\) = \(\dfrac{1}{6}\)
d, -2,5 + | 3x + 5 | = -1,5
e, \(\dfrac{1}{5}\) - | \(\dfrac{1}{5}\) - x | =\(\dfrac{1}{5}\)
Câu 1. Tính:
a, (\(\dfrac{3}{7}\)+\(\dfrac{1}{2}\))\(^2\)
b, (\(\dfrac{3}{4}\)- \(\dfrac{5}{6}\))\(^2\)
c, \(\dfrac{5^4.20^4}{25^5.4^5}\)
d, ( \(\dfrac{-10}{3}\))\(^5\).( \(\dfrac{-6}{5}\))\(^4\)
Câu 2. Tính:
a, (1+\(\dfrac{2}{3}\)-\(\dfrac{1}{4}\)). (\(\dfrac{4}{5}\)-\(\dfrac{3}{4}\))
b, 2: (\(\dfrac{1}{2}\)-\(\dfrac{2}{3}\))\(^3\)
Câu 3. Tìm số tự nhiên n, biết:
8\(^n\) : 2\(^n\)= 4
tim x : (\(\dfrac{3}{5}\))\(^5\).x=(\(\dfrac{3}{7}\))\(^7\)
Cho G; \(\dfrac{5}{3}\)+\(\dfrac{8}{3^2}\)+.\(\dfrac{11}{3^3}\).+....+ \(\dfrac{302}{3^{100}}\)
CMR; 2\(\dfrac{5}{9}\) bé hơn G lớn hơn 3\(\dfrac{1}{2}\)
5. \(3-1\dfrac{1}{2}-x+\dfrac{5}{4}=2-\left|1\dfrac{1}{8}-\dfrac{5}{12}\right|\) 6. \(3\dfrac{1}{14}-5\dfrac{1}{3}-\dfrac{4}{7}+\dfrac{11}{21}=-\dfrac{1}{2}\) 7. \(\dfrac{11}{-40}+\dfrac{4}{5}-\left|\dfrac{3}{4}-1\dfrac{5}{12}\right|=\dfrac{3}{20}-X\)
Tính:
a) \(\dfrac{\left(5^4-5^3\right)^3}{125^5}\)
b) \(\dfrac{9^3}{\left(3^4-3^3\right)^2}\)
rút gọn biểu thức khi \(\dfrac{-3}{5}\)<x<\(\dfrac{1}{7}\)
a,A=|x-\(\dfrac{1}{7}\)|-|x+\(\dfrac{3}{5}\)|+\(\dfrac{4}{5}\)
b, B=|-x+\(\dfrac{1}{7}\)|+|-x-\(\dfrac{3}{5}\)|-\(\dfrac{2}{6}\)
Thực hiện phép tính: a) A=\(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}\)-\(\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
b) \(\frac{1}{1.6}\)+\(\frac{1}{6.11}\)+\(\frac{1}{11.6}\)+...+\(\frac{1}{96.101}\)