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( 44 x 52 x 60 ) : (11 x 13 x 15)
= 44 x 52 x 60 : 11 : 13 :15
= (44 : 11) x ( 52 : 13) x ( 60 : 15)
= 4 x 4 x 4
= 64
Ta có: \(\left|x+\frac{1}{2}\right|\ge0;\left|x+\frac{1}{6}\right|\ge0;...;\left|x+\frac{1}{110}\ge0\right|\)
=> \(\left|x+\frac{1}{2}\right|+\left|x+\frac{1}{6}\right|+...+\left|x+\frac{1}{100}\right|\ge0\)
=> 11x \(\ge\)0 => x\(\ge\)0
=> \(x+\frac{1}{2}>0;x+\frac{1}{6}>0;...;x+\frac{1}{110}>0\)
=> \(\left|x+\frac{1}{2}\right|=x+\frac{1}{2};\left|x+\frac{1}{6}\right|=x+\frac{1}{6};...;\left|x+\frac{1}{110}\right|=x+\frac{1}{110}\)
=> \(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{6}\right)+...+\left(x+\frac{1}{110}\right)=11x\)
=> 10x + \(\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{110}\right)=11x\)
=> 10x + \(\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{10.11}\right)\)= 11x
=> 10x + \(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}\right)\)= 11x
=> 10x + \(\frac{10}{11}\)= 11x
=> x = \(\frac{10}{11}\)
Vậy x = \(\frac{10}{11}\)
Đặt \(A=1+5^2+5^4+...+5^{40}\)
\(\Rightarrow25A=5^2+5^4+5^6+...+5^{42}\)
Lấy \(25A-A=\left(5^2+5^4+5^6+...+5^{42}\right)-\left(1+5^2+5^4+...+5^{40}\right)\)
\(\Rightarrow24A=5^{42}-1\)
\(\Rightarrow A=\dfrac{5^{42}-1}{24}\)
Pt<=>x=120−18y11=11−y−7y+111Pt<=>x=120−18y11=11−y−7y+111
Vì x∈Z=>7y+1=11u(u∈Z)=>y=11u−17=2u−1−3(u−2)7x∈Z=>7y+1=11u(u∈Z)=>y=11u−17=2u−1−3(u−2)7
Mà u∈Zu∈Z
(3,7)=1(3,7)=1
=>u=7t+2(t∈Z)=>u=7t+2(t∈Z) =>y=11t+3=>x=6−18t=>y=11t+3=>x=6−18t
11x+(15-x)=5
phá ngoặc ta có:
11x+15-x=5
(11-1)x=5-15
10x=-10
x=-10:10
x=-1
\(a,9234:\left[3\cdot3\cdot\left(1+8^3\right)\right]\\ =9234:\left[9\cdot\left(1+512\right)\right]\\ =9234:\left(9\cdot513\right)\\ =9234:4617\\ =2\\ b,76-\left\{2\cdot\left[2\cdot5^2-\left(31-2\cdot3\right)\right]\right\}+3\cdot25\\ =76-\left\{2\cdot\left[2\cdot25-\left(31-6\right)\right]\right\}+75\\ =76-\left[2\cdot\left(50-25\right)\right]+75\\ =76-\left(2\cdot25\right)+75\\ =76-50+75\\ =26+75\\ =-49\)
(11x+52).809=8010..........................
=> 11x + 25 = 80......................
=> 11x =55.........................
=> x= 5...........................
(11x+52).809=8010..........................
=> 11x + 25 = 80......................
=> 11x =55.........................
=> x= 5...........................