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P = 1 + ( 22 + 23 ) + ( 24 + 25 ) + ( 26 + 27 )
P = 1 + 2 . ( 1 + 2 ) + 2 . ( 1 + 2 ) + 2 . ( 1 + 2 )
P = 1 + 2 . 3 + 2 . 3 + 2 . 3
Mỗi cặp đều có số 3
=> P = 1 + 22 + 23 + 24 + 25 + 26 + 27 chia hết cho 3
\(P=1+2^2+2^3+2^4+2^5+2^6+2^7\)
\(P=1+\left(2^2+2^3\right)+\left(2^4+2^5\right)+\left(2^6+2^7\right)\)
\(P=1+2^2\left(1+3\right)+2^4\left(1+2\right)+2^6\left(1+2\right)\)
\(P=1+2^2.3+2^4.3+2^6.3\)
\(P=\left(1+2^2+2^4+2^6\right).3⋮3\left(đpcm\right)\)
Ta có:
VT: \(\left(a+b\right)^2=\left(a+b\right)\left(a+b\right)\)
\(=a^2-ab-ab+b^2=a^2-2ab+b^2=VP\)
\(\Rightarrow\left(a+b\right)^2=a^2-2ab+b^2\left(đpcm\right)\)
hok tốt!!
\(E=\dfrac{-1}{3}-\dfrac{2}{3}+\dfrac{2}{5}-\dfrac{3}{5}+\dfrac{1}{5}=-1\)
Lời giải:
a.
$2(x-51)=7^{83}:7^{82}+20010=7+20010=20017$
$x-51=10008,5$
$x=10008,5+51=10059,5$
b.
$x-4x=1+600:(-6)$
$-3x=-99$
$x=\frac{-99}{-3}=33$
\(a,\Rightarrow2\left(x-51\right)=7+20010=20017\\ \Rightarrow x-51=\dfrac{20017}{2}\\ \Rightarrow x=\dfrac{20119}{2}\\ b,\Rightarrow-3x=1-100=-99\\ \Rightarrow x=33\)
a)\(\dfrac{-2}{17}+\dfrac{8}{17}=\dfrac{6}{17}\)
b) \(\dfrac{-9}{16}+\dfrac{7}{24}=\dfrac{-13}{48}\)
c)\(\dfrac{1}{8}+\dfrac{-5}{6}+\dfrac{7}{-36}=\dfrac{-17}{24}+\dfrac{7}{-36}=\dfrac{-65}{72}\)
a) =\(\dfrac{-2+8}{17}=\dfrac{6}{17}\)
b) =\(\dfrac{-27}{48}+\dfrac{14}{48}=\dfrac{-27+14}{48}=\dfrac{-13}{48}\)
c) \(=\dfrac{9}{72}+\dfrac{-60}{72}+\dfrac{-14}{72}=\dfrac{9+\left(-60\right)+\left(-14\right)}{72}=\dfrac{-65}{72}\)