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bài 4 :
a, 4.7.76 + 28.24 = 28.76 + 28. 24 = 28.( 76 + 24 ) = 28. 100 = 2800
b, 1 + 6 + 11 + 16 +...+ 46 + 51
dãy trên có SSH : ( 51 -1 ) :5 +1 = 11
tổng dãy trên : ( 1 + 51 ) x 11 : 2 = 286
c, 1 +2 -3 -4 + 5 +6 -7-8 +... - 299 - 300 + 301 + 302
= 1 + ( 2-3 -4 +5 ) + ( 6-7-8 +9 ) +... + ( 298 -299 -300 +301 ) + 302
= 1 + 302 = 303
a: x=-5/11+2/11=-3/11
b: =>x=-3/24+20/24+1/24=18/24=3/4
c: =>5/8-x=1/9+5/4=4/36+45/36=49/36
=>x=5/8-49/36=-53/72
d: =>2/3-x=1/3
=>x=1/3
e: =>1/5:x=12/35
=>x=7/12
\(a)x=\dfrac{1}{4}+\dfrac{5}{13}=\dfrac{33}{52}.\\ b)\dfrac{x}{3}=\dfrac{2}{3}+\dfrac{-1}{7}.\\ \Leftrightarrow\dfrac{x}{3}=\dfrac{11}{21}.\\ \Leftrightarrow\dfrac{7x}{21}=\dfrac{11}{21}.\\ \Rightarrow7x=11.\\ \Leftrightarrow x=\dfrac{11}{7}.\\ c)\dfrac{x}{3}=\dfrac{16}{24}+\dfrac{24}{36}=\dfrac{2}{3}+\dfrac{2}{3}=\dfrac{4}{3}.\\ \Rightarrow x=4.\\ d)\dfrac{x}{15}=\dfrac{1}{5}+\dfrac{2}{3}=\dfrac{13}{15}.\\ \Rightarrow x=13.\)
a, (-25) + 276 - (276 - 25)
= (-25) + 276 - 276 + 25
= [ (-25) + 25] - (276 - 276)
= 0 - 0
= 0
b, 24 x 46 + 24 x 53 + 24
= 24 x ( 46 + 53 + 1)
= 24 x 100
= 2400
17 - 2x = -15
2x = 17 - (-15)
2x = 32
x = 32 : 2
x = 16
--------
54 : (x + 2) = -6
x + 2 = 54 : (-6)
x + 2 = -9
x = -9 - 2
x = -11
--------
12.(3 - x) = 72
3 - x = 72 : 12
3 - x = 6
x = 3 - 6
x = -3
-------
-3(x + 5) + 18 = -27
-3(x + 5) = -27 - 18
-3(x + 5) = -45
x + 5 = -45 : (-3)
x + 5 = 15
x = 15 - 5
x = 10
-------
(x + 5)² = 9
x + 5 = 3 hoặc x + 5 = -3
*) x + 5 = 3
x = 3 - 5
x = -2
*) x + 5 = -3
x = -3 - 5
x = -8
Vậy x = -8; x = -2
--------
(3 - x)³ = 27
(3 - x)³ = 3³
3 - x = 3
x = 3 - 3
x = 0
a: =>(x-2)^3*[(x-2)^8-1]=0
=>(x-2)(x-3)(x-1)=0
=>\(x\in\left\{2;3;1\right\}\)
b: (x-5)^24=(x-5)^9
=>\(\left(x-5\right)^9\cdot\left[\left(x-5\right)^{15}-1\right]=0\)
=>x-5=0 hoặc x-5=1
=>x=6 hoặc x=5
c: =>(x-5)^4*[(x-5)^21-1]=0
=>x-5=0 hoặc x-5=1
=>x=5 hoặc x=6
a) \(\left(x-2\right)^{11}=\left(x-2\right)^3\)
\(\Rightarrow\left(x-2\right)^{11}-\left(x-2\right)^3=0\)
\(\Rightarrow\left(x-2\right)^3\left[\left(x-2\right)^8-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^3=0\\\left(x-2\right)^8-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\\left(x-2\right)^8=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x-2=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
b) \(\left(x-5\right)^{24}=\left(x-5\right)^9\)
\(\Rightarrow\left(x-5\right)^{24}-\left(x-5\right)^9=0\)
\(\Rightarrow\left(x-5\right)^9\left[\left(x-5\right)^{15}-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-5\right)^9=0\\\left(x-5\right)^{15}-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-5=0\\\left(x-5\right)^{15}=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=5\\x-5=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)
c) \(\left(x-5\right)^{25}=\left(x-5\right)^4\)
\(\Rightarrow\left(x-5\right)^{25}-\left(x-5\right)^4\)
\(\Rightarrow\left(x-5\right)^4\left[\left(x-5\right)^{21}-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-5\right)^4=0\\\left(x-5\right)^{21}-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-5=0\\\left(x-5\right)^{21}=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=5\\x-5=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)