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Số tập hợp còn là 4
\(\left(x+2\right)\left(x-5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+2=0\\x-5=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=5\end{cases}}}\)
câu 1: số tập hợp con của F là 4 câu 2: (x+2)(x-5)=0 => x+2=0 hoặc x-5=0 => x=-2 hoặc x=5
a) \(\left(-2\right)+\left(-12\right)+17+...+\left(-52\right)+57\) \(57\)
\(\Leftrightarrow\left(\left(-2\right)+7\right)+\left(\left(-12\right)+17\right)+...+\left(\left(-52\right)+57\right)\)
\(\Leftrightarrow5+5+...+5=5\times6=30\)
b) 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 +... - 79 - 80 - 81
= (1 + 2 - 3 - 4) + (5 + 6 - 7 - 8) +...+ (77 + 78 - 79 - 80) - 81
= -4 + (-4) +...+ (-4) - 81
= -4 . 20 - 81
= -80 - 81 = -161
1/ (a – b + c) – (a + c) = -b
a-b+c-a-c=-b
-b=-b
2/ (a + b) – (b – a) + c = 2a + c
a+b-b+a+c=2a+c
2a+c=2a+c
3/ - (a + b – c) + (a – b – c) = -2b
-a-b+c+a-b-c=-2b
-(b.2)=-2b
-2b=-2b
4/ a(b + c) – a(b + d) = a(c – d)
ab+ac-ab+ad=a(c-d)
ac-ad=a(c-d)
a(c-d)=a(c-d)
5/ a(b – c) + a(d + c) = a(b + d)
ab-ac+ad+ac=a(b+d)
ab+ad=a(b+d)
a(b+d)=a(b+d)
6/ a.(b – c) – a.(b + d) = -a.( c + d)
ab-ac-ab=ad=-a(c+d)
-ac+ad=-a(c+d)
-a(c+d)=-a(c+d)
a) |2x + 1| - 19 = -7
=> \(\left|2x+1\right|=-7+19=12\)
=> \(\left[{}\begin{matrix}2x+1=12\\2x+1=-12\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}2x=12-1=11\\2x=-12-1=-13\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=\frac{11}{2}\\x=-\frac{13}{2}\end{matrix}\right.\)
Vậy:............
b) -28 – 7. |- 3x + 15| = -70
=> \(\text{7. |- 3x + 15| = -28 - (-70) = -28 + 70 = 42}\)
=> \(\left|-3x+15\right|=42:7=6\)
=> \(\left[{}\begin{matrix}-3x+15=6\\-3x+15=-6\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}-3x=6-15=-9\\-3x=-6-15=-6+\left(-15\right)=-21\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=-9:\left(-3\right)=3\\x=x=-21:\left(-3\right)=7\end{matrix}\right.\)
Vậy:.....................
c) |18 – 2. |-x + 5|| = 12
=> \(\left[{}\begin{matrix}18-2.\left|-x+5\right|=12\\18-2.\left|-x+5\right|=-12\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}2.\left|-x+5\right|=18-12=6\\2.\left|-x+5\right|=18-\left(-12\right)=18+12=30\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}\left|-x+5\right|=6:2=3\\\left|-x+5\right|=30:2=15\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}\left[{}\begin{matrix}-x+5=3\\-x+5=-3\end{matrix}\right.\\\left[{}\begin{matrix}-x+5=15\\-x+5=-15\end{matrix}\right.\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}\left[{}\begin{matrix}-x=3-5=-2\\-x=-3-5=-8\end{matrix}\right.\\\left[{}\begin{matrix}-x=15-5=10\\-x=-15-5=-20\end{matrix}\right.\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}\left[{}\begin{matrix}x=2\\x=8\end{matrix}\right.\\\left[{}\begin{matrix}x=-10\\x=20\end{matrix}\right.\end{matrix}\right.\)
\(S=1+4+4^2+...+4^{49}\)
\(4S=4+4^2+...+4^{50}\)
\(4S-S=4^{50}-1\)
\(3S=4^{50}-1\)
\(S=\frac{4^{50}-1}{3}\)
Hc tốt
\(S=1+4+4^2+...+4^{49}\)
\(4S=\left(4+4^2+...+4^{50}\right)\)
\(4S-S=3S=\left(4+4^2+...+4^{50}\right)-\left(1+4+4^2+...+4^{49}\right)=4^{50}-1\)
\(\Rightarrow S=\frac{4^{50}-1}{3}\)
\(A=3+3^2+3^3+...+3^{2021}\)
\(\Rightarrow A+1=1+3+3^2+3^3+...+3^{2021}\)
\(A+1=\left(1+3+3^2\right)+\left(3^3+3^4+3^5\right)+...+\left(3^{2019}+3^{2020}+3^{2021}\right)\)
\(A+1=\left(1+3+3^2\right)+3^3\left(1+3+3^2\right)+...+3^{2019}\left(1+3+3^2\right)\)
\(A+1=13.3^3.13+...+3^{2019}.13\)
\(A+1=13\left(1+3^3+...+3^{2019}\right)\)
\(\Rightarrow A+1⋮13\)
\(\Rightarrow A:13d\text{ư}12\)
ta có :
A = 3 + 32 + ( 33 +34 + 35 ) + ( 36 + 37 + 38 ) + ... + ( 32019 +32020 + 32021 )
Đặt B = ( 33 +34 + 35 ) + ( 36 + 37 + 38 ) + ... + ( 32019 +32020 + 32021 )
B = 351 + ( 33 .33 + 33 . 34 + 33 .35 ) + .... + ( 32016 .33 + 32016 .34 + 32016 . 35 )
B = 351 + 351 . 33 + ... + 351 .32016
B = 351 ( 1 + 33 + ... + 32016 ) \(⋮\)11
Thay B vào A => 3 + 32 + B chia 11 dư 3 + 32
ta có 3 + 32 = 3 + 9
= 12
mà 12 \(\equiv\)-1 ( mod 13 )
Vậy A chia 13 dư -1
học CLB toán à : > ? có bài nào hay hay ib mk nha ^^
Học tốt
#Gấu
1/ ab + ac = a.(b + c)
2/ ab – ac + ad = a.(b - c + d)
3/ ax – bx – cx + dx = x.(a - b - c + d)
4/ a(b + c) – d(b + c) = (b + c)(a - d)
5/ ac – ad + bc – bd = a.(c - d) + b.(c - d) = (c - d)(a + b)
6/ ax + by + bx + ay = x.(a + b) + y.(a + b) = (a + b)(x.y)
a) 500
b) 2303
c) 537
d) 35000
e) 90000
f) 380