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a) \(\frac{1}{2}-\left(\frac{1}{3}+\frac{1}{4}\right)< x< \frac{1}{48}-\left(\frac{1}{16}-\frac{1}{6}\right)\)
Ta có: 1/2 - (1/3 + 1/4) = 1/2 - 7/12 = -1/12 ;
1/48 - (1/16 - 1/6) = 1/48 + 5/48 = 1/8
Vì \(-\frac{1}{12}< x< \frac{1}{8}\) nên x = 0
b) \(4\frac{5}{9}:2\frac{5}{18}-7< x< \left(3\frac{1}{5}:3,2+4,5.1\frac{31}{45}\right):\left(-21\frac{2}{3}\right)\)
Ta có :
\(4\frac{5}{9}:2\frac{5}{18}-7=2-7=-5\)
\(\left(3\frac{1}{5}:3,2+4,5.1\frac{31}{45}\right):\left(-21\frac{2}{3}\right)=\left(1+\frac{38}{5}\right):\left(-21\frac{2}{3}\right)=\frac{43}{5}:\frac{-65}{3}=-\frac{129}{325}\)
Vì \(-5< x< -\frac{129}{325}\) nên \(x\in\left\{-4;-3;-2;-1\right\}\)
a) Dễ thấy VT > 0;mà VT=VP
=>VP > 0 => 4x > 0=> x > 0
=>\(\left|x+\frac{1}{2}\right|=x+\frac{1}{2};\left|x+\frac{1}{3}\right|=x+\frac{1}{3};\left|x+\frac{1}{6}\right|=x+\frac{1}{6}\)
=>BT đầu tương đương \(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{3}\right)+\left(x+\frac{1}{6}\right)=4x\)
\(=>3x+1=4x=>x=1\)
a) Để đẳng thức xảy ra thì: x>0 (vì: \(\left|x+\frac{1}{2}\right|+\left|x+\frac{1}{3}\right|+\left|x+\frac{1}{6}\right|>0\) )
Khi đó: \(\left|x+\frac{1}{2}\right|=x+\frac{1}{2};\left|x+\frac{1}{3}\right|=x+\frac{1}{3};\left|x+\frac{1}{6}\right|=x+\frac{1}{6}\)
=>\(x+\frac{1}{2}+x+\frac{1}{3}+x+\frac{1}{6}=4x\)
<=>x=1
Vậy x=1
b)Điều kiện: \(x\ne-3;-10;-21;-34\)
\(\frac{7}{\left(x+3\right)\left(x+10\right)}+\frac{11}{\left(x+10\right)\left(x+21\right)}+\frac{13}{\left(x+21\right)\left(x+34\right)}=\frac{x}{\left(x+3\right)\left(x+34\right)}\)
<=>\(\frac{1}{x+3}-\frac{1}{x+10}+\frac{1}{x+10}-\frac{1}{x+21}+\frac{1}{x+21}-\frac{1}{x+34}=\frac{x}{\left(x+3\right)\left(x+34\right)}\)
<=>\(\frac{1}{x+3}-\frac{1}{x+34}=\frac{x}{\left(x+3\right)\left(x+34\right)}\)
=>x+34-x-3=x
<=>x=31 (nhận)
Vậy x=31
a) \(=\frac{\left(-2\right)^{10}}{\left(-2\right)^7}=\frac{\left(-2\right)^7.\left(-2\right)^3}{\left(-2\right)^7}=\left(-2\right)^3=-8\)
b) \(=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2.3}=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2.3}=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{12}.3^{10}.\left(3^2-2^{-11}.3^{-9}\right)}=\frac{6}{3^2-2^{-11}.3^{-9}}\)
\(=\frac{2.3}{3.\left(3-2^{-11}.3^{-10}\right)}=\frac{2}{3-2^{-11}.3^{-10}}\)
a) -90/189 + 45/84 - 78/126
= -10/21 + 15/28 - 13/21
= (-10/21 - 13/21) + 15/28
= -24/21 + 15/28
= -17/28
b) \(\frac{\frac{2}{3}+\frac{5}{7}+\frac{4}{21}}{\frac{5}{6}+\frac{11}{7}-\frac{7}{21}}\)
\(=\frac{\frac{29}{21}+\frac{4}{21}}{\frac{101}{42}-\frac{7}{21}}\)
\(=\frac{\frac{11}{7}}{\frac{29}{14}}\)
\(=\frac{22}{29}.\)
Chúc bạn học tốt!
Giả sử \(A< B\)\(\Leftrightarrow\)\(B-A>0\) ta có :
\(B-A=\left(1^2+3^2+5^2+...+19^2+21^2\right)-\left(2^2+4^2+6^2+...+18^2+20^2\right)\)
\(B-A=\left(3^2-2^2\right)+\left(5^2-4^2\right)+...+\left(19^2-18^2\right)+\left(21^2-20^2\right)+1\)
\(B-A=\left(3-2\right)\left(3+2\right)+...+\left(19-18\right)\left(19+18\right)+\left(21-20\right)\left(21+20\right)+1\)
\(B-A=2+3+4+5+18+19+20+21+1>0\)
Vậy điều giả sử đúng hay \(A< B\)
Chúc bạn học tốt ~
2)
a) \(\frac{1}{3}x-\left(-\frac{2}{3}\right)^2=\sqrt{\frac{16}{81}}\)
\(\Rightarrow\frac{1}{3}x-\frac{4}{9}=\frac{4}{9}\)
\(\Rightarrow\frac{1}{3}x=\frac{4}{9}+\frac{4}{9}\)
\(\Rightarrow\frac{1}{3}x=\frac{8}{9}\)
\(\Rightarrow x=\frac{8}{9}:\frac{1}{3}\)
\(\Rightarrow x=\frac{8}{3}\)
Vậy \(x=\frac{8}{3}.\)
b) \(4x-\frac{2}{5}+\frac{3}{4}=\frac{11}{4}\)
\(\Rightarrow4x-\frac{2}{5}=\frac{11}{4}-\frac{3}{4}\)
\(\Rightarrow4x-\frac{2}{5}=2\)
\(\Rightarrow4x=2+\frac{2}{5}\)
\(\Rightarrow4x=\frac{12}{5}\)
\(\Rightarrow x=\frac{12}{5}:4\)
\(\Rightarrow x=\frac{3}{5}\)
Vậy \(x=\frac{3}{5}.\)
Chúc bạn học tốt!
\(\frac{2^8\cdot3^{21}+2^{18}\cdot3^6}{2^{10}\cdot2^{21}+2^{20}\cdot3^6}=\frac{2^8\cdot3^6\left(3^{27}+2^{10}\right)}{2^{20}\left(2^{11}+3^6\right)}=\frac{3^6\left(3^{27}+2^{10}\right)}{2^{12}\left(2^{11}+3^6\right)}\)