Tính
a) \(A=1+\left(5+1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
b) \(B=10^2+8^2+.....+2^2-\left(9^2+7^2+5^2+3^2+1^2\right)\)
a,\(\frac{-1}{24}-\left[\frac{1}{4}-\left(\frac{1}{2}-\frac{7}{8}\right)\right]\)
b,\(\left[\frac{5}{7}-\frac{7}{5}\right]-\left[\frac{1}{2}-\left(\frac{-2}{7}-\frac{1}{10}\right)\right]\)
c,\(\left(\frac{-1}{2}\right)-\left(\frac{-3}{5}\right)+\left(\frac{-1}{9}\right)+\frac{1}{71}-\left(\frac{-2}{7}\right)+\frac{4}{35}-\frac{7}{8}\)
d,\(\left(3-\frac{1}{4}+\frac{2}{3}\right)-\left(5-\frac{1}{3}-\frac{6}{5}\right)-\left(6-\frac{7}{4}+\frac{3}{2}\right)\)
e,\(\left(\frac{1}{2}-\frac{13}{14}\right):\frac{5}{7}-\left(\frac{-2}{21}+\frac{1}{7}\right):\frac{5}{7}\)
g,\(\frac{4}{9}:\left(\frac{-1}{7}\right)+6\frac{5}{9}:\left(\frac{-1}{7}\right)\)
Tính:
\(A=\sqrt{20}-10\sqrt{\dfrac{1}{5}}+\sqrt{\left(\sqrt{5}-1\right)^2}\)
\(B=2\sqrt{32}+5\sqrt{8}-4\sqrt{32}\)
\(C=\sqrt{\left(3-\sqrt{2}^2\right)}-\sqrt{\left(1-\sqrt{2}\right)^2}\)
\(D=\sqrt{\left(5-1\right)^2}+\sqrt{\left(\sqrt{5}-3\right)^2}\)
\(E=\left(3+\dfrac{5-\sqrt{5}}{\sqrt{5}-1}\right)\left(3-\dfrac{5+\sqrt{5}}{\sqrt{5}-1}\right)\)
\(F=\sqrt{6+2\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
\(G=\dfrac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}+\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\)
\(H=\dfrac{10}{\sqrt{3}-1}-\dfrac{55}{2\sqrt{3}+1}\)
help
a) Ta có: \(A=\sqrt{20}-10\sqrt{\dfrac{1}{5}}+\sqrt{\left(\sqrt{5}-1\right)^2}\)
\(=2\sqrt{5}-2\sqrt{5}+\sqrt{5}-1\)
\(=\sqrt{5}-1\)
b) Ta có: \(B=2\sqrt{32}+5\sqrt{8}-4\sqrt{32}\)
\(=8\sqrt{2}+10\sqrt{2}-16\sqrt{2}\)
\(=2\sqrt{2}\)
Tính nhanh giá trị của biểu thức:
\(A=\dfrac{\left(2^4+2^2+1\right)\left(4^4+4^2+1\right)\left(6^4+6^2+1\right)\left(8^4+8^2+1\right)\left(10^4+10^2+1\right)}{\left(3^4+3^2+1\right)\left(5^4+5^2+1\right)\left(7^4+7^2+1\right)\left(9^4+9^2+1\right)\left(11^4+11^2+1\right)}\)
\(\left(\frac{-5}{12}+\frac{7}{4}-\frac{3}{8}\right)-\left[4\frac{1}{2}-7\frac{1}{3}\right]-\left(\frac{1}{4}-\frac{5}{2}\right)\)
\(\left[2\frac{1}{4}-5\frac{3}{2}\right]-\left(\frac{3}{10}-1\right)-5\frac{1}{2}+\left(\frac{1}{3}-\frac{5}{6}\right)\)
\(\frac{4}{7}-\left(3\frac{2}{5}-1\frac{1}{2}\right)-\frac{5}{21}+\left[3\frac{1}{2}-4\frac{2}{3}\right]\)
\(\frac{1}{8}-1\frac{3}{4}+\left(\frac{7}{8}-3\frac{7}{2}+\frac{3}{4}\right)-\left[\frac{7}{4}-\frac{5}{8}\right]\)
\(\left(\frac{3}{5}-2\frac{1}{10}+\frac{11}{20}\right)-\left[\frac{-3}{4}+1\frac{7}{2}\right]\)
\(\left[-2\frac{1}{5}-2\frac{2}{3}\right]-\left(\frac{1}{15}-5\frac{1}{2}\right)+\left[\frac{-1}{6}+\frac{1}{3}\right]\)
\(1\frac{1}{8}-\left(\frac{1}{15}-\frac{1}{2}+\frac{-1}{6}\right)+\left[\frac{5}{4}+\frac{3}{2}\right]\)
\(\frac{5}{6}-\left(1\frac{1}{3}-1\frac{1}{2}\right)+\left[\frac{5}{12}-\frac{3}{4}-\frac{1}{6}\right]\)
\(1\frac{1}{4}-\left(\frac{7}{12}-\frac{2}{3}-1\frac{3}{8}\right)+\left[\frac{5}{24}-2\frac{1}{2}\right]-\frac{1}{6}-\left[\frac{-3}{4}\right]\)
\(-2\frac{1}{5}+2\frac{3}{10}-\left(\frac{6}{20}-\left[\frac{2}{8}-1\frac{1}{2}\right]\right)+\left[\frac{7}{20}-1\frac{1}{4}\right]\)
\(-\left[1\frac{2}{3}-3\frac{1}{2}+\frac{1}{4}\right]+\left(\frac{2}{6}-\frac{5}{12}\right)-\left(\frac{1}{3}-\left[\frac{1}{4}-\frac{1}{3}\right]\right)\)
\(-\frac{4}{5}-\left(1\frac{1}{10}-\frac{7}{10}\right)+\left[\frac{3}{4}-1\frac{1}{5}\right]+1\frac{1}{2}\)
\(\frac{3}{21}-\frac{5}{14}+\left[1\frac{1}{3}-5\frac{1}{2}+\frac{5}{14}\right]-\left(\frac{1}{6}-\frac{3}{7}+\frac{1}{3}\right)\)
\(-1\frac{2}{5}+\left[1\frac{3}{10}-\frac{7}{20}-1\frac{1}{4}\right]-\left(\frac{1}{5}-\left[\frac{3}{4}-1\frac{1}{2}\right]\right)\)
\(2\frac{1}{3}-\left(\frac{1}{2}-2\frac{1}{6}+\frac{3}{4}\right)+\left[\frac{5}{12}-1\frac{1}{3}\right]-\frac{7}{8}+3\frac{1}{2}\)
\(2\frac{1}{4}-1\frac{3}{5}-\left(\frac{9}{20}-\frac{7}{10}\right)+\left[1\frac{3}{5}-2\frac{1}{2}\right]+\frac{3}{4}\)
\(\left[\frac{8}{3}-5\frac{1}{4}+\frac{1}{6}\right]-\frac{7}{4}+\frac{-5}{12}-\left(1-1\frac{1}{2}+\frac{1}{3}\right)\)
\(\left(\frac{1}{4}-\left[1\frac{1}{4}-\frac{7}{10}\right]+\frac{1}{2}\right)-2\frac{1}{5}-1\frac{3}{10}+\left[1-\frac{1}{2}\right]\)
TRÌNH BÀY GIÚP MÌNH NHA
Tối giản phân số sau bằng cách thuận tiện:
\(\frac{\left(2^4+2^2+1\right)\left(4^4+4^2+1\right)\left(6^4+6^2+1\right)\left(8^4+8^2+1\right)\left(10^4+10^2+1\right)}{\left(3^4+3^2+1\right)\left(5^4+5^2+1\right)\left(7^4+7^2+1\right)\left(9^4+9^2+1\right)\left(11^4+11^2+1\right)}\)
\(=\frac{21.273.1333.4161.10101}{91.651.2451.6643.14763}\)
\(=\frac{3.7.13.21.31.43.73.57.91.111}{7.13.21.31.43.57.73.91.111.133}=\frac{3}{133}\)
Tuy nhiên cách làm trên phải có máy tính mới làm đc:
Có thể sử dụng công thức:
\(x^4+x^2+1=\left(x^2+x+1\right)\left(x^2-x+1\right)\)
Sau đó phân h:
\(2^4+2^2+1=\left(2^2+2+1\right)\left(2^2-2+1\right)=7.3\)
\(4^4+4^2+1=\left(4^2+4+1\right)\left(4^2-4+1\right)=21.13\)
....Tiếp tực làm thì sẽ ra đc kết quả:
\(=\frac{3.7.13.21.31.43.73.57.91.111}{7.13.21.31.43.57.73.91.111.133}=\frac{3}{133}\)
BT7: Tính
\(3,C=\left(5-1\right)\left(5+1\right)\left(5^2+1\right)\left(5^4+1\right)...\left(5^{16}+1\right)\)
\(4,D=15\left(4^2+1\right)\left(4^4+1\right)...\left(4^{64}+1\right)\)
\(5,E=24\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)...\left(5^{128}+1\right)+\left(5^{256}-1\right)\)
3: =(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)
=(5^4-1)(5^4+1)(5^8+1)(5^16+1)
=(5^8-1)(5^8+1)(5^16+1)
=(5^16-1)(5^16+1)
=5^32-1
4:
D=(4^4-1)(4^4+1)(4^8+1)*....*(4^64+1)
=(4^8-1)(4^8+1)*...*(4^64+1)
=...
=4^128-1
5: =(5^2-1)(5^2+1)(5^4+1)*...*(5^128+1)+(5^256-1)
=(5^4-1)(5^4+1)*...*(5^128+1)+5^256-1
=5^256-1+5^256-1
=2*5^256-2
3, \(C=\left(5-1\right)\left(5+1\right)\left(5^2+1\right)\left(5^4+1\right)....\left(5^{16}+1\right)\)
\(C=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)....\left(5^{16}+1\right)\)
\(C=\left(5^4-1\right)\left(5^4+1\right)....\left(5^{16}+1\right)\)
\(C=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(C=\left(5^{16}-1\right)\left(5^{16}+1\right)\)
\(C=5^{32}-1\)
4, \(D=15\left(4^2+1\right)\left(4^4+1\right)...\left(4^{64}+1\right)\)
\(D=\left(4^2-1\right)\left(4^2+1\right)\left(4^4+1\right)...\left(4^{64}+1\right)\)
\(D=\left(4^4-1\right)\left(4^4+1\right)...\left(4^{64}+1\right)\)
\(D=\left(4^8-1\right)\left(4^8+1\right)...\left(4^{64}+1\right)\)
\(D=\left(4^{16}-1\right)\left(4^{16}+1\right)...\left(4^{64}+1\right)\)
\(D=\left(4^{32}-1\right)\left(4^{32}+1\right)\left(4^{64}+1\right)\)
\(D=\left(4^{64}-1\right)\left(4^{64}+1\right)\)
\(D=4^{128}-1\)
5, \(E=24\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)...\left(5^{256}+1\right)\)
\(E=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)...\left(5^{128}+1\right)\left(5^{256}+1\right)\)
\(E=\left(5^4-1\right)\left(5^4+1\right)....\left(5^{256}+1\right)\)
....
\(E=\left(5^{128}-1\right)\left(5^{128}+1\right)\left(5^{256}+1\right)\)
\(E=\left(5^{256}-1\right)\left(5^{256}+1\right)\)
\(E=5^{512}-1\)
Tính nhanh:
a) \(1^2-2^2+3^2-4^2+5^2-6^2+...+2011^2-2012^2\)
b) \(10\left(9^2+1\right)\left(9^4+1\right)\left(9^8+1\right)\left(9^{16}+1\right)\left(9^{32}+1\right)-9^{64}\)
thực hiên phép tính :
a, \(\left(3^2\right)^2-\left(2^3\right)^2-\left(-5^2\right)^2\)
b, \(2^3+3.\left(-\dfrac{1}{2}\right)^0-\left(\dfrac{1}{2}\right)^2.4+\left(\left(-2\right)^2:\dfrac{1}{2}\right):8\)
c, \(\left(4.2^5\right):\left(2^3.\dfrac{1}{16}\right)\)
d, \(A=\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(a, \)\(\left(3^2\right)^2-\left(2^3\right)^2-\left(-5^2\right)^2=9^2-8^2-10^2\)
= \(81-64-100\)
\(=-83\)
\(b,\)\(2^3+3.\left(-\dfrac{1}{2}\right)^0-\left(\dfrac{1}{2}\right)^2.4+\left(\left(-2\right)^2:\dfrac{1}{2}\right):8=8+3.1-\dfrac{1}{4}.4+\left(4:\dfrac{1}{2}\right):8\) \(=8+3-1+8:8\)
\(=8+3-1+1\)
\(=11\)
Bài 1: Tính:
A=\(\left(-2\right).\left(-3\right)-5.\left|-5\right|+125.\left(\dfrac{-1}{5}\right)^2\)
B=\(\left(-3\right).\left|-7\right|-\left(-4\right).\left|5\right|+\dfrac{1}{3}.\left|-9\right|\)
C=\(\left(-2\right)^3.\left|-3\right|-\dfrac{1}{5}.\left|-25\right|-4.\left|-7\right|+\left(-2\right)^2\)
D=\(\left(-6\right).\left|-3\right|+2.\left|-9\right|-7\left|\left(-2\right)^3\right|+8.\left|-7\right|\)
E=\(\left|-3^2\right|.\left|4\right|-\left|7\right|.8-\left|6\right|.\left|-8\right|-\left|12\right|.\left(\dfrac{1}{2}\right)^2\)
Bài 2: Tìm x:
a)\(12-2\left|3x+2\right|=10\)
b)\(2.\left|5-4x\right|+17=\left(-2\right)^3.\left(-4\right)\)
c)\(\left|3x-5\right|+\left(-3\right)^2.2=12.\left|3x+5\right|+117\)
d)\(4.\left|3-2x\right|+\left(-5\right).\left|4-3x\right|-5=-6\)
e)\(\left|2x-7\right|-2^3.\left|2x-7\right|+15=-5.\left|2x-7\right|+3\)
f)\(\left|x+2\right|+\left|x^2-4\right|=0\)
g)\(\left|3x-9\right|+\left|x^2-9\right|=0\)
h)\(\left|2x-1\right|+\left|x^2-\dfrac{1}{4}\right|=0\)
1. A = (-2)(-3) - 5.|-5| + 125.\(\left(-\dfrac{1}{5}\right)^2\)
= 6 - 25 + 125.\(\dfrac{1}{25}\)
= -19 + 5
= -14
@Shine Anna
1. B = (-3).|-7| - (-4).|5| + \(\dfrac{1}{3}.\left|-9\right|\)
= -21 + 20 + 3
= 2
@Shine Anna