bài 1
(4^2+1)(4^4+1)(4^8+1)(4^16+1)(4^32+1)-1/15*4^64
Bài 2:Cho x+1/x=10. Tính S=x^5+1/x^5
BÀI 1 - Tính
a (0,8)^5/(0,4)^6
b 8^10+4^10/8^4+4^11
BÀI 2 - Tìm x ϵ Z
a 2^x-1 = 16
b (x-1)^2 = 25
c (x-1)^x+2 = (x-1)^x+6
d (x+20)^100 + I y+4 I = 0
Bài 1:
a)\(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}=\frac{\left(0,2\cdot4\right)^5}{\left(0,2\cdot2\right)^6}=\frac{\left(0,2\right)^5\cdot\left(2^2\right)^5}{\left(0,2\right)^6\cdot2^6}=\frac{\left(0,2\right)^5\cdot2^{10}}{\left(0,2\right)^6\cdot2^6}=\frac{2^4}{0,2}=\frac{16}{\frac{2}{10}}=80\)
b)\(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(1+2^{10}\right)}=\frac{2^{20}}{2^{12}}=256\)
Bài 2:
a)\(2^{x-1}=16\)
\(\Rightarrow2^{x-1}=2^4\)
\(\Rightarrow x-1=4\Rightarrow x=5\)
b)\(\left(x-1\right)^2=25\)
\(\Rightarrow\left(x-1\right)^2=5^2=\left(-5\right)^2\)
\(\Rightarrow x-1=5\) hoặc \(x-1=-5\)
\(\Rightarrow x=6\) hoặc \(x=-4\)
Vậy \(x=6\) hoặc \(x=-4\)
c)\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+6}\)
\(\Rightarrow\left(x-1\right)^{x+2}-\left(x-1\right)^{x+6}=0\)
\(\Leftrightarrow\left(x-1\right)^{x+2}\left[1-\left(x-1\right)^4\right]\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}\left(x-1\right)^{x+2}=0\\1-\left(x-1\right)^4=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x-1=0\\1=\left(x-1\right)^4\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=1\\\left(x-1\right)^4=\left(-1\right)^4=1^4\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=1\\x-1=1\\x-1=-1\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=1\\x=2\\x=0\end{array}\right.\)
d)\(\left(x+20\right)^{100}+\left|y+4\right|=0\left(1\right)\)
Ta thấy: \(\begin{cases}\left(x+20\right)^{100}\ge0\\\left|y+4\right|\ge0\end{cases}\)
\(\Rightarrow\left(x+20\right)^{100}+\left|y+4\right|\ge0\left(2\right)\)
Từ (1) và (2) suy ra \(\begin{cases}\left(x+20\right)^{100}=0\\\left|y+4\right|=0\end{cases}\)
\(\Rightarrow\begin{cases}x+20=0\\y+4=0\end{cases}\)\(\Rightarrow\begin{cases}x=-20\\y=-4\end{cases}\)
Tính hợp lí nếu có thể:
a)3/7+4/9+4/7+5/9
b)1/5+4/10+9/15+16/20+25/25+36/30+49/35+64/40+81/45
c)1/8+1/12+3/8+5/12
d)(1-1/2)x(1-1/3)x(1-1/4)x...x(1-100)
e)9/5:17/15+8/5:17/15
f)2/1x2+2/2x3+2/3x4+...+2/19x20
Ai nhanh nhất mình tick cho
a) 3/7 + 4/9 + 4/7 + 5/9
= ( 3/7 + 4/7 ) + ( 4/9 + 5/9 )
= 7/7 + 9/9
= 1 + 1
= 2
b)1/5 + 4/10 + 9/15 + 16/20 + 25/25 + 36/30 + 49/35 + 64/40 + 81/45
= 1/5 + 2/5 + 3/5 + 4/5 + 5/5 + 6/5 + 7/5 + 8/5 + 9/5
= ( 1/5 + 9/5 ) + ( 2/5 + 8/5 ) + (7/5 + 3/5 ) + ( 4/5 + 6/5 ) + 5/5
= 2 + 2 + 2 + 2 + 1
= 2 x 4 + 1
= 8 +1
= 9
c) 1/8 + 1/12 + 3/8 + 5/12
= ( 1/8 + 3/8 ) + ( 1/12 + 5/12)
= 4/8 + 6/12
= 1/2 + 1/2
= 2/4 = 1/2
mỏi tay rồi
d; (1 - \(\dfrac{1}{2}\)) x (1 - \(\dfrac{1}{3}\)) x (1 - \(\dfrac{1}{4}\)) x ... x ( 1 - \(\dfrac{1}{100}\))
= \(\dfrac{1}{2}\) x \(\dfrac{2}{3}\) x \(\dfrac{3}{4}\) x \(\dfrac{3}{4}\) x ... x \(\dfrac{99}{100}\)
= \(\dfrac{1}{100}\)
e; \(\dfrac{9}{5}\) : \(\dfrac{17}{15}\) + \(\dfrac{8}{5}\) : \(\dfrac{17}{15}\)
= \(\dfrac{9}{5}\) x \(\dfrac{15}{17}\) + \(\dfrac{8}{5}\) x \(\dfrac{15}{17}\)
= \(\dfrac{27}{17}\) + \(\dfrac{24}{17}\)
= \(\dfrac{51}{17}\)
= 3
Bài 1: Tính 1) 52 + (-2) 2) (-24) + (-7) 3) 16 - 70 4) (-23) - (-77) Bài 2: Tính một cách hợp lí 1) (-48) + 25 +46 + 48 2) 10.(-8).20.(-25) 3) 165.(-45) + 45.(-35) Bài 3: Tìm số nguyên x biết a) 24 + x = 13 b) 3x + 8 = 20 Bài 4: Tính giá trị của các biểu thức a) (-48) : 3 b) 540 : (-1) 8) 200 - (-120) + (-80) 2 PHIẾU BÀI TẬP TUẦN 18 Thời gian nộp bài 17h ngày 09/01/2022 5) 80 + (-320) 6) (-15) .8 7) (-16).(-5) 9 ) 9 8 - 5 0 7 3 . 2 4) (-6) + (-23) + 31 + (-2) 5) 180 + (-36) + 2021 + (-144) 6) 8 + (-3) + 12 + (-15) + 20 + (-22) c) 4x – 20 = 5.42 d, 27 - 3(x-2) = -15 c) 840 : (-24) d) (-96) : (-6)
Bài 3:
a: =>x=13-24=-11
b: =>3x=12
hay x=4
bài 1:Tìm x
1 - (5|4/9+x - 7|7/18 ) :15|3/4 = 0
x +1/2 +1/4 +1/8 + 1/16 + 1/32 +1/64 +1/128 /1/3*4 +1/4*5 +1/5*6 +1/6*7 +1/7*8 + 1/8*9
ai chả lời nhanh nhất mk sẽ tích cho và kết bạn đầu tiên
troi cac anh chi ko biet sao : 1 - (49/9 + x - 133/18 ) :63 /4 = 0
( 49/9 -133/18 ) :63/4 =1 ( boi vi 1 -1 = 0 ma cho nen ta coi phan nay = 1 )
49/9+ x - 133/18 = 63/4
49/9 + x = 63/4 + 133/18
49/9 + x = 833/36
x = 833/36 - 49/9
x =637/36
-5/8=x/16
Y/10=(-4)/8
Bai 8:
1) x/3-1/4=(-5)/6
2) x+3/15=1/3
3) x-12/4=1/2
4) 3/4x=1/2
BÀI 1 :
a) \(-\frac{5}{8}=\frac{x}{16}\)
\(\Rightarrow x=\frac{5.16}{-8}=\frac{80}{-8}=-10\)
b) \(\frac{y}{10}=-\frac{4}{8}\)
\(\Rightarrow y=\frac{-4.10}{8}=-\frac{40}{8}=-5\)
bài 8
1) \(\frac{x}{3}-\frac{1}{4}=-\frac{5}{6}\)
\(\frac{x}{3}=-\frac{5}{6}+\frac{1}{4}\)
\(\frac{x}{3}=-\frac{7}{12}\)
\(\Rightarrow x=-\frac{7.3}{12}=-\frac{21}{12}=-\frac{7}{4}\)
2) \(x+\frac{3}{15}=\frac{1}{3}\)
\(x=\frac{1}{3}+\frac{3}{15}\)
\(x=\frac{8}{15}\)
3) \(x-\frac{12}{4}=\frac{1}{2}\)
\(x=\frac{1}{2}+\frac{12}{4}\)
\(x=\frac{7}{2}\)
4) \(\frac{3}{4}x=\frac{1}{2}\)
\(x=\frac{3}{4}:\frac{1}{2}\)
\(x=\frac{3}{2}\)
Bài 1: Làm tính nhân
a) -3x^2 . ( 2x^3 - 2x + 1/3 )
b) ( x^4 + 2x^3 - 2/3 ) . ( -3x^4 )
c) ( x + 3 ) . ( x - 4 )
d) ( x - 4 ) . ( x^2 + 4x + 16 )
e) 4. ( x - 1/2 ) . ( x + 1/2 ) . ( 4x^2 + 1 )
Bài 2: Tìm x, biết
a) ( 2 - x ) . (x^2 + 2x + 4 ) + x . ( x - 3 ) . ( x + 4 ) - x^2 + 24 = 0
b) (x/2 + 3 ) . ( 5 - 6x ) + ( 12x - 2 ) . ( x/4 + 3 ) = 0
Bài 1: Làm tính nhân
a) -3x^2 . ( 2x^3 - 2x + 1/3 )
b) ( x^4 + 2x^3 - 2/3 ) . ( -3x^4 )
c) ( x + 3 ) . ( x - 4 )
d) ( x - 4 ) . ( x^2 + 4x + 16 )
e) 4. ( x - 1/2 ) . ( x + 1/2 ) . ( 4x^2 + 1 )
Bài 2: Tìm x, biết
a) ( 2 - x ) . (x^2 + 2x + 4 ) + x . ( x - 3 ) . ( x + 4 ) - x^2 + 24 = 0
b) (x/2 + 3 ) . ( 5 - 6x ) + ( 12x - 2 ) . ( x/4 + 3 ) = 0
1a) -3x2(2x3 - 2x + 1/3) = -6x5 + 6x3 - x2
b) (x4 + 2x3 - 2/3).(-3x4) = -3x8 - 6x7 + 2x4
c) (x + 3)(x - 4) = x2 - 4x + 3x - 12 = x2 - x - 12
d)(x - 4)(x2 + 4x + 16) = (x - 4)(x2 + 4x + 42) = x3 - 64
e) 4(x - 1/2)(x + 1/2)(4x2 + 1) =4(x2 - 1/4)(4x2 + 1) = 4(4x4 + x2 - x2 - 1/4) = 4(4x4 - 1/4) = 16x4 - 1
B2. a) (2 - x)(x2 + 2x + 4) + x(x - 3)(x + 4) - x2 + 24 = 0
=> 8 - x3 + x(x2 + 4x - 3x - 12) - x2 + 24 = 0
=> 8 - x3 + x3 + x2 - 12x - x2 + 24 = 0
=> -12x + 32 = 0
=> -12x = -32
=> x = -32 : (-12) = 8/3
b) (x/2 + 3)(5 - 6x) + (12x - 2)(x/4 + 3) = 0
=> 5x/2 - 3x2 + 15 - 18x + 3x2 + 36x - x/2 - 6 = 0
=> 20x + 9 = 0
=> 20x = -9
=> x = -9/20
Tính nhanh :
3^8 x 5^8 - ( 15^4-1 ) x ( 15^4 + 1 )
( 2+ 1 ) x ( 2^2 + 1 ) x ( 2^4 + 1 ) x ... x ( 2^16 +1 ) +1
Viết các biểu thức sau dưới dạng một lũy thừa:
6; 3/2 x 9/4 x 81/16
7; (1/2)^7 x 8 x 32 x 2^8
8; (-1/7)^4 x 125 x 5
9; 4 x 32 : (2^3 x 1/16)
10; (1/7)^2 x 1/7 x 49
\(\dfrac{3}{2}\times\dfrac{9}{4}\times\dfrac{81}{16}=\dfrac{3}{2}\times\left(\dfrac{3}{2}\right)^2\times\left(\dfrac{3}{2}\right)^4=\left(\dfrac{3}{2}\right)^7\)
\(\left(\dfrac{1}{2}\right)^7\times8\times32\times2^8=\left(\dfrac{1}{2}\right)^7\times2^3\times2^5\times2^8=\left(\dfrac{1}{7}\right)^7\times2^{16}\)
\(\left(-\dfrac{1}{7}\right)^4\times125\times5=\left(-\dfrac{1}{7}\right)^4\times5^3\times5=\left(-\dfrac{1}{7}\right)^4\times5^4\)
\(4\times32:\left(2^3\times\dfrac{1}{16}\right)=2^2\times2^5:2^3:2^{-4}=2^0\)
\(\left(\dfrac{1}{7}\right)^2\times\dfrac{1}{7}\times49=\left(\dfrac{1}{7}\right)^3\times7^3=1^3\)
6, \(\dfrac{3}{2}\times\dfrac{9}{4}\times\dfrac{81}{16}=\dfrac{3}{2}\times\left(\dfrac{3}{2}\right)^2\times\left(\dfrac{3}{2}\right)^4\)
7,\(\left(\dfrac{1}{2}\right)^7\times8\times32\times2^8=\left(\dfrac{1}{2}\right)^7\times2^3\times2^5\times2^8\)
8,\(\left(-\dfrac{1}{7}\right) ^4\times125\times5=\left(\dfrac{1}{7}\right)^4\times5^3\times5\)
9,\(4\times32:\left(2^3\times\dfrac{1}{16}\right)=2^2\times2^5:\left[2^3\times\left(\dfrac{1}{2}\right)^4\right]\)
10, \(\left(\dfrac{1}{7}\right)^2\times\dfrac{1}{7}\times49=\left(\dfrac{1}{7}\right)^2\times\dfrac{1}{7}\times7^2\)
6) \(...=\dfrac{3}{2}.\left(\dfrac{3}{2}\right)^2.\left(\dfrac{3}{2}\right)^4=\left(\dfrac{3}{2}\right)^7\)
7) \(...=2^{-7}.2^3.2^5.2^8=2^9\)
8) \(...=\left(\dfrac{1}{7}\right)^4.5^3.5=\left(\dfrac{1}{7}\right)^4.5^4\)
9) \(...=2^2.2^5:\left(2^3.2^{-4}\right)=2^8\)
10) \(...=\left(\dfrac{1}{7}\right)^3.\left(\dfrac{1}{7}\right)^2=\left(\dfrac{1}{7}\right)^5\)