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Bài 2:
a)|x| < 3
x\(\in\){-2;-1;0;1;2}
b)|x - 4 | < 3
x\(\in\){ 6 ; 5 ; 4 ; 3 ; 2 }
c) | x + 10 | < 2
x\(\in\){ -2 ; -10 }
Bài 1:
A = 1 + 2 - 3 + 4 + 5 - 6 +...+98 - 99
A = (1 + 4 + 7 +...+97) + [(2-3)+(5-6)+...+(98-99)]
A = 1617 + [(-1)+(-1)+...+(-1)]
A = 1617 + (-49)
A = +(1617-49) = A = 1568
B = - 2 - 4 + 6 - 8 + 10 + 12 - .... + 60
B =
2)
a) \(x\in\left\{2;1;0;-1;-2\right\}\)
b) \(x\in\left\{6;-6;5;-5;4\right\}\)
c) \(x\in\left\{-9;-11;-10\right\}\)
3)
\(\left(a;b\right)\in\left\{\left(0;1\right);\left(0;-1\right);\left(1;0\right);\left(-1;0\right)\right\}\)
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( 3x - 6 ) . 3 = 18
3x - 6 = 18 : 3 = 6
3x = 6 + 6 = 12
x= 4
6x - 5 = 613
6x = 613 + 5 =618
x=103
x-36:18=12
x - 2 = 12
x= 12 + 2
x= 14
\(\left(3x-6\right).3=18\)
\(\Rightarrow3x-6=19:3=6\)
\(\Rightarrow3x=6+6=12\)
\(\Rightarrow x=12:3=4\)
\(6.x-5=613\)
\(\Rightarrow6x=613+ 5=618\)
\(\Rightarrow x=618:6=103\)
\(x-36:18=12\)
\(\Rightarrow x-2=12\)
\(\Rightarrow x=12+2=14\)
Ủng hộ nha m.n ^_^
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(2x + 1)(y-5) = 12
Ta có: 12 = 1.12 = 2.6 = 3.4 = (-1)(-12) = (-2) (-6) = (-3) (-4)
Bận liệt ke ra nhé
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(3x-12).(x-3)=0
=> 3x-12=0 hoặc x-3=0
bạn tự giải 2 trường hợp đó ra
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(14,78-a)/(2,87+a)=4/1
14,78+2,87=17,65
Tổng số phần bằng nhau là 4+1=5
Mỗi phần có giá trị bằng 17,65/5=3,53
=>2,87+a=3,53
=>a=0,66.
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Ta có
\(\left(2x-1\right)^2\ge0\) với mọi x
\(\Rightarrow3\left(2x-1\right)^2\ge0\)
\(\Rightarrow5+3\left(2x-1\right)^2\ge5\)
Dấu " = " xáy ra khi 2x+1=0
=>x=-1/2
Vậy MINC=5 khi x= - 1/2
\(5+3\left(2x-1\right)^2\)
\(5+3\left[\left(2x^2\right)-2.2x.1+1^2\right]\)
\(\Rightarrow\left(2x-1\right)^2\ge0\)
\(\Rightarrow8\left(2x-1\right)^2\ge8\)
Vậy giá trị nhỏ nhất là 8
Khi 2x - 1 = 0
2x = 1
x = 1/2
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1, Tìm x :
a, \(x^7.x^5=3^{12}\)
\(\Rightarrow x^{12}=3^{12}\)
\(\Rightarrow x=3\)
Vậy x = 3
b, \(\left(x+1\right)^4=5^8\div25^4\)
\(\left(x+1\right)^4=5^8\div\left(5^2\right)^4\)
\(\left(x+1\right)^4=5^8\div5^8\)
\(\left(x+1\right)^4=1\)
\(\Rightarrow x\in\left\{0;1\right\}\)
Vậy \(x\in\left\{0;1\right\}\)
c, \(x^6=x\)
\(\Rightarrow x^6-x=0\)
\(\Rightarrow x.x^5-x.1=0\)
\(\Rightarrow x\left(x^5-1\right)=0\)
x = 0 hoặc x5 - 1 = 0
x = 0 hoặc x5= 1
x = 0 hoặc x5 = 1
\(\Rightarrow x\in\left\{0;1\right\}\)
Vậy \(x\in\left\{0;1\right\}\)
2, Tính :
\(\left(4^{20}+4^{15}\right)\div\left(4^{10}+4^5\right)\)
\(=4^{15}.\left(4^5+1\right)\div4^5.\left(4^5+1\right)\)
\(=4^{15}\div4^5\)
\(=4^{10}\)
Vậy giá trị biểu thức trên bằng 410
\(A=2^0+2^1+2^2+...+2^{2016}\)
\(2A=2+2^2+2^3+...+2^{2017}\)
\(2A-A=\left(2+2^2+2^3+...+2^{2017}\right)-\left(2^0+2^1+2^2+...+2^{2016}\right)\)
\(\Rightarrow A=2^{2017}-1\)
Vậy : \(A=2^{2017}-1\)
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Bài 1 :
A = 12 + 22 + 32 +....+n2
A = 12 + 2.(1+1) + 3.(2 +1) + 4.( 3 +1) +.....+n(n-1 + 1)
A = 1 + 1.2 + 2 + 2.3 + 3 + 3.4 + 4 +.....+ n.(n-1) + n
A = ( 1 + 2 + 3 + 4 +....+n) + ( 1.2 + 2.3 + 3.4 +....+(n-1).n
A = (n+1).{(n-1):n+1)/2 +1/3.[1.2.3 +2.3.3 +.....+(n-1)n.3]
A = (n+1).n/2+1/3.[1.2.3 +2.3.(4-1)+ ...+(n-1).n [(n+1) - (n -2)]
A = (n+1)n/2+1/3.( 1.2.3 + 2.3.4 -1.2.3 +..+ (n-1)n(n+1)- (n-2)(n-1)n)
A =(n+1)n/2 + 1/3.(n-1)n(n+1)
A = n(n+1)[1/2 + 1/3 .(n-1)]
A = n.(n+1) \(\dfrac{3+2n-2}{6}\)
A= n.(n+1)(2n+1)/6
Bài 2 :
a, (x+1) +(x+2) + (x+3)+...+(x+10) = 5070
(x+10 +x+1).{( x+10 - x -1): 1 +1):2 = 5070
(2x + 11)10 : 2 = 5070
( 2x + 11)5 = 5070
2x+ 11 = 5070:5
2x = 1014 - 11
2x = 1003
x = 1003 :2
x = 501,5
b, 1 + 2 + 3 +...+x = 820
( x + 1)[ (x-1):1 +1] : 2 = 820
(x +1).x = 820 x 2
(x +1).x = 1640
(x +1) .x = 40 x 41
x = 40
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Ví X chia hết cho 12,Xchia hết cho 10 nên X thuộc BC(12;10)
Mà BCNN(10:12) =60 nên X thuộc:...;-240;-180;-120;-60;0;60;120;180;240;...
Mà X>-200 và X<200 nên X thuộc -180;-120;-60;0;60;120;180
NHỚ K NHÁ
\(\dfrac{\left(x+3\right)}{6}=\dfrac{10}{12}\)
\(=>\dfrac{\left(x+3\right)}{6}=\dfrac{5}{6}\)
\(=>x+3=5\)
\(=>x=2\)