Tìm x biết
a) \(\left(\frac{4}{9}\right)^x=\left(\frac{8}{27}\right)^6\)
b) \(\left(\frac{1}{9}\right)^x=\left(\frac{1}{27}\right)^{22}\)
Ai làm nhanh đúng 3 tick
tìm x biết \(8\left(x+\frac{1}{x}\right)^2+4\left(x^2+\frac{1}{x^2}\right)^2-4\left(x^2+\frac{1}{x^2}\right)\left(x+\frac{1}{x}\right)^2=\left(x+4\right)^2...\)
ai làm nhanh và đúng thì đc 3 tick nha
đó chính là -4 minh khong muon giai ra ta lau lam ban
rút 4 ra ngoài nhan bạn 4(2(x+1/x)^2+(x^2+1/x^2)^2-(x^2+1/x^2)(x+1/x)^2=(x+4)^2
mik xét cái này cho dễ nhìn nhan
2(x+1/x)^2-(x^2+1/x^2)(x+1/x)^2
= (x+1/x)^2(2-x^2-1/x^2)
= -(x+1/x)^2(x^2-2+1/x^2)
= -(x+1/x)^2(x-1/x)^2=-(x^2-1/x^2)^2
thế ở trên ta có
4(-(x^2-1/x^2)^2+(x^2+1/x^2)^2)=(x+4)^2
4(-x^4+2-1/x^4+x^4+2+1/x^4)=x^2+8x+16
4.4=x^2+8x+16
suy ra x^2+8x=0
x(x+8)=0
suy ra x=0 hoặc x=-8
mak nhìn để bài thì x=0 ko được nên x=-8
Tìm x biết : \(\left(\frac{1}{3}\right)^x\left(\frac{1}{9}\right)^x\left(\frac{1}{27}\right)^x\left(\frac{1}{81}\right)^x\left(\frac{1}{243}\right)^x=\left(-\frac{1}{3}\right)^{30}\)
\(a,\left(-3\right)^{x+3}=-\frac{1}{27}\)
\(b,\left(-6\right)^{2x+2}=\frac{1}{36}\)
\(c,\left(-3\right)^{x+5}=\frac{1}{81}\)
\(d,\left(\frac{1}{9}^x\right)=\left(\frac{1}{27}\right)^6\)
\(e,\left(\frac{4}{9}\right)^x=\left(\frac{8}{27}\right)^6\)
\(f,5^{x+4}-3.5^{x+3}=2.5^{11}\)
\(r,4.3^{x-1}+2.3^{x+2}=4.3^6+2.3^9\)
\(h,\left(\frac{1}{2}-\frac{1}{3}\right).6x+6^{x+2}=6^{10}+6^7\)
nhờ mấy bn giúp mk tối mình nộp rồi
a)\(\left(-3\right)^{x+3}=-\frac{1}{27}\)
\(\left(-3\right)^{x+3}=\left(-\frac{1}{3}\right)^3\)
\(\left(-3\right)^{x+3}=\left(-\frac{3^0}{3^1}\right)^3\)
\(\left(-3\right)^{x+3}=\left(-3^{-1}\right)^3\)
\(\left(-3\right)^{x+3}=\left(-3\right)^{-3}\)
\(\Rightarrow x+3=-3\)
\(\Rightarrow x=-6\)
b)\(\left(-6\right)^{2x+2}=\frac{1}{36}\)
\(\left(-6\right)^{2x+2}=\left(-\frac{1}{6}\right)^2\)
\(\left(-6\right)^{2x+2}=\left(-\frac{6^0}{6^1}\right)^2\)
\(\left(-6\right)^{2x+2}=\left(-6^{-1}\right)^2\)
\(\left(-6\right)^{2x+2}=\left(-6\right)^{-2}\)
\(\Rightarrow2x+2=-2\)
\(\Rightarrow2x=-4\)
\(\Rightarrow x=-2\)
c)\(\left(-3\right)^{x+5}=\frac{1}{81}\)
\(\left(-3\right)^{x+5}=\left(-\frac{1}{3}\right)^4\)
\(\left(-3\right)^{x+5}=\left(-\frac{3^0}{3^1}\right)^4\)
\(\left(-3\right)^{x+5}=\left(-3^{-1}\right)^4\)
\(\left(-3\right)^{x+5}=\left(-3\right)^{-4}\)
\(\Rightarrow x+5=-4\)
\(\Rightarrow x=-9\)
d)\(\left(\frac{1}{9}\right)^x=\left(\frac{1}{27}\right)^6\)
\(\left[\left(\frac{1}{3}\right)^2\right]^x=\left[\left(\frac{1}{3}\right)^3\right]^6\)
\(\left(\frac{1}{3}\right)^{2x}=\left(\frac{1}{3}\right)^{18}\)
\(\Rightarrow2x=18\)
\(\Rightarrow x=9\)
e)\(\left(\frac{4}{9}\right)^x=\left(\frac{8}{27}\right)^6\)
\(\left[\left(\frac{2}{3}\right)^2\right]^x=\left[\left(\frac{2}{3}\right)^3\right]^6\)
\(\left(\frac{2}{3}\right)^{2x}=\left(\frac{2}{3}\right)^{18}\)
\(\Rightarrow2x=18\)
\(\Rightarrow x=9\)
f)\(5^{x+4}-3\cdot5^{x+3}=2\cdot5^{11}\)
\(5^{x+3}\cdot5-3\cdot5^{x+3}=2\cdot5^{11}\)
\(5^{x+3}\left(5-3\right)=2\cdot5^{11}\)
\(5^{x+3}\cdot2=2\cdot5^{11}\)
\(\Rightarrow5^{x+3}=5^{11}\)
\(\Rightarrow x+3=11\)
\(\Rightarrow x=8\)
r)\(4\cdot3^{x-1}+2\cdot3^{x+2}=4\cdot3^6+2\cdot3^9\)
\(4\cdot3^x:3+2\cdot3^x\cdot9=4.3^7:3+2\cdot3^7\cdot9\)
\(3^x\left(4:3+2\cdot9\right)=3^7\left(4:3+2\cdot9\right)\)
\(\Rightarrow3^x=3^7\)
\(\Rightarrow x=7\)
Tìm x biết
\(|x+\frac{1}{3}|+\frac{4}{5}=|\left(-3,2\right)+\frac{2}{5}|+\left(27-\frac{3}{5}\right)\left(27-\frac{3^2}{6}\right)\left(27-\frac{3^3}{7}\right)...\left(27-\frac{3^{2010}}{2014}\right)\)
\(\left|x+\frac{1}{3}\right|+\frac{4}{5}=\left|-3,2+\frac{2}{5}\right|+\left(27-\frac{3}{5}\right)\left(27-\frac{3^2}{6}\right)...\left(27-\frac{3^5}{9}\right)...\left(27-\frac{3^{2010}}{2014}\right)\)
\(\Leftrightarrow\left|x+\frac{1}{3}\right|+\frac{4}{5}=\frac{14}{5}+\left(27-\frac{3^2}{6}\right)\left(27-\frac{3^3}{7}\right)...\left(27-27\right)...\left(27-\frac{3^{2010}}{2014}\right)\)
\(\Leftrightarrow\left|x+\frac{1}{3}\right|+\frac{4}{5}=\frac{14}{5}\)
\(\Leftrightarrow\left|x+\frac{1}{3}\right|=2\)
\(\Rightarrow\hept{\begin{cases}x+\frac{1}{3}=2\\x+\frac{1}{3}=-2\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{5}{3}\\x=-\frac{7}{3}\end{cases}}}\)
bạn ơi, có một chỗ chưa chuẩn .bạn kiểm tra lại giú mình. chỗ vế trái bạn thiếu \(\left(27-\frac{3}{5}\right)\). bạn bổ sung vào cho đúng nhé. dù sao vẫn cảm ơn bạn.
a)A=\(\frac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}\) b)B=\(\frac{45}{19}-\left(\frac{1}{2}\left(\frac{1}{3}+\left(\frac{1}{4}\right)^{-1}\right)^-\right)^{-1}\) c)C=\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^{10}.6^{19}-7.2^{29}.27^6}\)
d)D=\(\frac{2^{21}.3^5-4^6.81}{\left(2^2.3\right)^6+8^4.3^5}\) e) E=\(\left(6^9.2^{10}+12^{10}\right):\left(2^{19}.27^3+15.4^9.9^4\right)\)
f) F=\(\frac{3^6.45^4-15^{13}.5^{-9}}{27^4.24^3+45^6}\) g)G=\(\frac{\left(\frac{2}{5}\right)^7.5^7+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7.5^2+512}\) h)H=\(x+\frac{0,2-0,375+\frac{5}{11}}{-0,3+\frac{9}{16}-\frac{15}{22}}\)với x=-1/3
ai nhanh nhất mà trả lời dúng mik tặng 3 k
tìm x,y :
\(\frac{1}{2}-\left(6\frac{5}{9}+x-\frac{117}{8}\right):\left(12\frac{1}{9}\right)=0\)
\(\left(y+\frac{1}{3}\right)+\left(y+\frac{2}{9}\right)+\left(y+\frac{1}{27}\right)+\left(y+\frac{1}{81}\right)=\frac{56}{81}\)
1, \(\frac{1}{2}-\left(6\frac{5}{9}+x-\frac{117}{8}\right):\left(12\frac{1}{9}\right)=0\)
\(\left(\frac{6.9+5}{9}+x-\frac{117}{8}\right):\frac{12.9+1}{9}=\frac{1}{2}\)
( . là nhân nha)
\(\left(\frac{59}{9}-\frac{117}{8}+x\right):\frac{109}{9}=\frac{1}{2}\)
\(\frac{59}{9}-\frac{117}{8}+x=\frac{1}{2}\cdot\frac{109}{9}\)
\(\frac{59}{9}-\frac{117}{8}+x=\frac{109}{18}\)
\(x=\frac{109}{18}-\frac{59}{9}+\frac{117}{8}\)
\(x=\frac{113}{8}\)
( \(\left(y+\frac{1}{3}\right)+\left(y+\frac{2}{9}\right)+\left(y+\frac{1}{27}\right)+\left(y+\frac{1}{81}\right)=\frac{56}{81}\)
\(y+\frac{1}{3}+y+\frac{2}{9}+y+\frac{1}{27}+y+\frac{1}{81}=\frac{56}{81}\)
\(4y+\frac{1}{3}+\frac{2}{9}+\frac{1}{27}+\frac{1}{81}=\frac{56}{81}\)
\(4y+\frac{49}{81}=\frac{56}{81}\)
\(4y=\frac{7}{81}\)
y = 7/81:4
y = 7/324
\(\frac{5}{9}:\left(\frac{1}{11}-\frac{5}{22}\right)+\frac{5}{9}:\left(\frac{1}{15}-\frac{2}{3}\right)\)
\(=\frac{5}{9}:\left(\frac{-3}{22}\right)+\frac{5}{9}:\left(-\frac{3}{5}\right)\)
\(=\frac{5}{9}.\left(\frac{-22}{3}\right)+\frac{5}{9}.\left(-\frac{5}{3}\right)\)
\(=-\frac{110}{27}+-\frac{25}{27}\)
\(=-5\)
Em làm thế đúng không các anh chị?
đúng đó nhưng bạn nên nhóm \(\frac{-22}{3}\)và \(\frac{-5}{3}\)vào với nhau và đặt \(\frac{5}{9}\)ra ngoài sẽ tính nhanh hơn
tìm x: \(\frac{\left(3x^2-27\right)\left(8x^2\right)6}{4\left(9-3x\right)\left(x^2+3x\right)}=\frac{\tan\left(x+4\right)}{log\left(x+\frac{1}{4}\right)}\)
Bài 1 thực hiện phép tính
a)\(\frac{45}{19}-\left(\frac{1}{2}+\left(\frac{1}{3}+\left(\frac{1}{4}\right)^{-1}\right)^{-1}\right)^{-1}.\)
b) \(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^{10}.6^{19}-7.2^{29}.27^6}.\)
Bài 2. tìm x, biết:
a) 2(x-1) - 3(2x+2) - 4(2x+3) =16
b) \(3\frac{1}{2}:\left|2x-1\right|=\frac{21}{22}\)
c) |x2+|x-1|| = x2+2
Bài 3. Chứng minh rằng số có dạng abcabc luôn chia hết cho 11
Bài 4.tính:
a) A = \(\left(\frac{0,4-\frac{2}{9}+\frac{2}{11}}{1,4-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-0,25+\frac{1}{5}}{1\frac{1}{6}-0,875+0,7}\right):\frac{2012}{2013}\)
b) B =\(4.\left(-\frac{1}{2}\right)^2-2.\left(-\frac{1}{2}\right)^2+3.\left(-\frac{1}{2}\right)+1\)
c) C =\(\frac{1}{2}:\left(-1\frac{1}{2}\right):1\frac{1}{3}:\left(-1\frac{1}{4}\right):1\frac{1}{5}:\left(-1\frac{1}{6}\right):...:\left(-1\frac{1}{100}\right)\)
d) D =\(\frac{4^6.9^5+6^9.120}{-8^4.3^{12}+6^{11}}\)