1 Tìm x:
a) \(2.2^2.2^3...2^x=1024\) b) \(\frac{37-x}{x+13}=\frac{3}{7}\)
2. Tính :
\(\frac{1}{2}\sqrt{64}-\sqrt{\frac{4}{25}}+\left(\frac{50^2-15.125}{5^4}\right)^{2014}\)
Câu 1 :
a)Tính \(\left(\frac{2}{5}\right)^{2014}:\left(\frac{4}{25}\right)^{1007}\) \(3^{n+1}\): 9 \(\frac{1}{2}\sqrt{64}-\sqrt{\frac{4}{25}}+\left(\frac{50^2-15.125}{5^4}\right)^{2014}\)
b)Tìm x: .\(2.2^2.2^3...2^x=1024\) \(\frac{37-x}{x+13}=\frac{3}{7}\)
giúp mình rồi ai đúng mình tick nhe
1. Tính : \(\left(\frac{2}{5}\right)^{2014}:\left(\frac{4}{25}\right)^{1007}\) \(3^{n+1}:9\) \(\frac{1}{2}\sqrt{64}-\sqrt{\frac{4}{5}}+\left(\frac{50^2-15.125}{5^4}\right)^{2014}\)
2. Tìm x: \(2.2^2.2^3...2^x=1024\) \(\frac{37-x}{x+13}=\frac{3}{7}\)
Giúp mình nhé ai làm đúng thì mình tick và kb
Tìm x, y, z
a) \(\sqrt{16}x+\frac{3}{4}=2\sqrt{\frac{4}{25}}+0,01.\sqrt{100}\)
b) \(\left|x\right|+3^2=2^2+\left(\frac{1}{2}\right)^3\)
c) \(2x\left(x-\frac{2}{3}\right)=0\)
d) \(\frac{37-x}{x+13}=\frac{3}{7}\)
a: \(\Leftrightarrow4x+\dfrac{3}{4}=2\cdot\dfrac{2}{5}+0.01\cdot10=\dfrac{9}{10}\)
=>4x=3/20
hay x=3/80
b: \(\Leftrightarrow\left|x\right|=4+\dfrac{1}{8}-9=-\dfrac{39}{8}\)(vô lý)
c: 2x(x-2/3)=0
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-\dfrac{2}{3}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{2}{3}\end{matrix}\right.\)
d: \(\dfrac{37-x}{x+13}=\dfrac{3}{7}\)
=>259-7x=3x+39
=>-10x=-220
hay x=22
1) Rút gọn biểu thức theo là cách hợp lý:
A = \(\frac{1-\frac{1}{\sqrt{49}}+\frac{1}{49}-\frac{1}{\left(7\sqrt{7}\right)^2}}{\frac{\sqrt{64}}{2}-\frac{4}{7}+\left(\frac{2}{7}\right)^2-\frac{4}{343}}\)
2) Tính hợp lý:
M = \(1-\frac{5}{\sqrt{196}}-\frac{5}{\left(2\sqrt{21}\right)^2}-\frac{\sqrt{25}}{204}-\frac{\left(\sqrt{5}\right)^2}{374}\)
3) Có hay không giá trị của x thỏa mãn điều kiện sau:
\(2002.\sqrt{\left(1+x\right)^2}+2003.\sqrt{\left(1-x\right)^2}=0\)
4) Tìm các số x, y, z thỏa mãn đẳng thức:
\(\sqrt{\left(x-\sqrt{2}\right)^2}+\sqrt{\left(y+\sqrt{2}\right)^2}+\left|x+y+z\right|=0\)
4) mấy bài kia trình bày dài lắm!! (lười ý mà ahihi)
\(\sqrt{\left(x-\sqrt{2}\right)^2}+\sqrt{\left(y+\sqrt{2}\right)^2}+|x+y+z|=0.\)
\(\Leftrightarrow|x-\sqrt{2}|+|y+\sqrt{2}|+|x+y+z|=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-\sqrt{2}=0\\y+\sqrt{2}=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\sqrt{2}\\y=-\sqrt{2}\end{cases}}}\)
Tìm z thì dễ rồi
a)\(\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}=\frac{x+1}{5}+\)\(\frac{x+1}{6}\)
b)\(\frac{x+1}{2009}+\frac{x+2}{2008}+\frac{x+3}{2007}=\)\(\frac{x+10}{2000}+\frac{x+11}{1999}+\frac{x+12}{1998}\)
c)\(2.2^2.2^3.2^4.........2^x=1024\)\(\left(x\in z\right)\)
Tìm x
b./ \(\Leftrightarrow\frac{x+1}{2009}+1+\frac{x+2}{2008}+1+\frac{x+3}{2007}+1=\frac{x+10}{2000}+1+\frac{x+11}{1999}+1+\frac{x+12}{1998}+1.\)
\(\Leftrightarrow\frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}-\frac{x+2010}{2000}-\frac{x+2010}{1999}-\frac{x+2010}{1998}=0\)
\(\Leftrightarrow\left(x+2010\right)\left(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{2007}-\frac{1}{2000}-\frac{1}{1999}-\frac{1}{1998}\right)=0\)(b)
Mà \(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{2007}-\frac{1}{2000}-\frac{1}{1999}-\frac{1}{1998}< 0\)
(b) \(\Leftrightarrow x+2010=0\Leftrightarrow x=-2010\)
a./
\(\Leftrightarrow\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}-\frac{x+1}{5}-\frac{x+1}{6}=0.\)
\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\right)=0\)(a)
Mà \(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}>0\)
(a) \(\Leftrightarrow x+1=0\Leftrightarrow x=-1\)
c./ \(\Leftrightarrow2\cdot2^2\cdot2^3\cdot...\cdot2^x=2^{10}\Leftrightarrow2^{1+2+3+...+x}=2^{10}\Leftrightarrow1+2+3+...+x=10\)
\(\Leftrightarrow\frac{x\left(x+1\right)}{2}=10\Leftrightarrow x\left(x+1\right)=20=4\cdot5\Rightarrow x=4\)
1.Chứng tỏ rằng:
A=75.(42004+42003+...+42+4+1)+25 chia hết cho 100
2.tính nhanh:
\(A=\frac{\left(1+2+3+...+99+100\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{7}-\frac{1}{9}\right)\left(63.1,2-21.3,6\right)}{1-2+3-4+...+99-100}\)
\(B=\frac{\left(\frac{1}{14}-\frac{\sqrt{2}}{7}+\frac{\sqrt[3]{2}}{35}\right).\left(-\frac{4}{15}\right)}{\left(\frac{1}{10}+\frac{\sqrt[3]{2}}{25}-\frac{\sqrt{2}}{5}\right).\frac{5}{7}}\)
3.a)tính giá trị của biểu thức A=3x2-2x+1 với |x|=\(\frac{1}{2}\)
b)Tìm x nguyên để \(\sqrt{x+1}\)chia hết cho \(\sqrt{x-3}\)
1. A = 75(42004 + 42003 +...+ 42 + 4 + 1) + 25
A = 25 . [3 . (42004 + 42003 +...+ 42 + 4 + 1) + 1]
A = 25 . (3 . 42004 + 3 . 42003 +...+ 3 . 42 + 3 . 4 + 3 + 1)
A = 25 . (3 . 42004 + 3 . 42003 +...+ 3 . 42 + 3 . 4 + 4)
A = 25 . 4 . (3 . 42003 + 3 . 42002 +...+ 3 . 4 + 3 + 1)
A =100 . (3 . 42003 + 3 . 42002 +...+ 3 . 4 + 3 + 1) \(⋮\) 100
3a) |x| = 1/2
=> x = 1/2 hoặc x = -1/2
với x = 1/2:
A = \(3.\left(\frac{1}{2}\right)^2-2.\frac{1}{2}+1\)
\(A=\frac{3}{4}-1+1=\frac{3}{4}\)
với x = -1/2
A = \(3.\left(-\frac{1}{2}\right)^2-2\left(-\frac{1}{2}\right)+1\)
\(A=\frac{3}{4}+1+1=\frac{3}{4}+2=\frac{11}{4}\)
2.
A=\(\frac{\left(1+2+3+.....+99+100\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{7}-\frac{1}{9}\right)\left(63.1,2-21.3,6\right)}{1-2+3-4+......+99-100}\)\
A=0
Tính
a) \(2\sqrt{\frac{25}{16}}-3\sqrt{\frac{49}{36}}+4\sqrt{\frac{81}{64}}\)
b) \(\left(3\sqrt{2}\right)^2-\left(4\sqrt{\frac{1}{2}}\right)^2+\frac{1}{16}.\left(\sqrt{\frac{3}{4}}\right)^2\)
c) \(\frac{2}{3}\sqrt{\frac{81}{16}}-\frac{3}{4}\sqrt{\frac{64}{9}}+\frac{7}{5}.\sqrt{\frac{25}{196}}\)
a) = \(\frac{7}{2}\)
b) = \(\frac{643}{64}\)
c) = 0
TÌM GIÁ TRỊ LỚN NHẤT (có thể dùng BĐT côsi)
\(y=\left|x\right|\sqrt{25-x^2}Với-5\le x\le5\)
\(f\left(x\right)=\frac{x}{2}+\sqrt{1-x-2x^2}\)
\(E=\frac{\sqrt{x-1}}{x}+\frac{\sqrt{y-2}}{y}+\frac{\sqrt{z-3}}{z}\)
TÍNH
\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
\(\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+\sqrt{1+\frac{1}{4^2}+\frac{1}{5^2}}+...+\sqrt{1+\frac{1}{2012^2}+\frac{1}{2013^2}}\)
GIÚP EM ĐI Ạ, MAI EM PHẢI KIỂM TRA RỒI
BT1: Tinh
\(1.A=\left(4-\frac{1}{2}+\frac{2}{3}\right)+\left(5+\frac{4}{3}-\frac{6}{5}\right)-\left(6-\frac{7}{4}+\frac{4}{5}\right)\)
\(2.B=\frac{\left(-1\right)^6.3^5.4^3}{9^2.2^5}\)
\(3.\frac{4}{5}.\frac{11}{3}-\frac{4}{5}.\frac{8}{3}+\frac{1}{5}\)
\(4.\sqrt{289-\sqrt{169+\sqrt{256-\sqrt{196}}}}\)
\(5.\frac{3^{15}.2^{18}.5^4}{6^{14}.10^5}\)