1+2+3+...+80-278
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\(A=1\times2+2\times3+3\times4+...+277\times278\)
\(3\times A=1\times2\times3+2\times3\times\left(4-1\right)+3\times4\times\left(5-2\right)+...+277\times278\times\left(279-276\right)\)
\(3\times A=1\times2\times3+2\times3\times4-1\times2\times3+...+277\times278\times279-276\times277\times278\)
\(3\times A=277\times278\times279\)
\(A=\frac{277\times278\times279}{3}=7161558\)
\(A=1\cdot2+2\cdot3+...+277\cdot278\)
\(3A=3\left(1\cdot2+2\cdot3+...+277\cdot278\right)\)
\(3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+277\cdot278\cdot\left(279-276\right)\)
\(3A=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+277\cdot278\cdot279-276\cdot277\cdot278\)
\(3A=277\cdot278\cdot279\Rightarrow A=\frac{277\cdot278\cdot279}{3}=7161558\)
\(12\left(x+5\right)+2x=130\\\Leftrightarrow 12x+60+2x=130\\ \Leftrightarrow14x=70\\ \Leftrightarrow x=5\\ ----\\ 23\left(x-5\right)-12x=138\\ \Leftrightarrow23x-115-12x=138\\ \Leftrightarrow23x-12x=138+115\\ \Leftrightarrow11x=253\\ \Leftrightarrow x=\dfrac{253}{11}=23\\ ----\\ 360-12x+23\left(x-5\right)=278\\ \Leftrightarrow360-12x+23x-115=278\\ \Leftrightarrow-12x+23x=278+115-360\\ \Leftrightarrow11x=33\\ \Leftrightarrow x=\dfrac{33}{11}=3\)
\(6\left(x+3\right)+3\left(x-5\right)=278\\ \Leftrightarrow6x+18-3x-15=278\\ \Leftrightarrow6x-3x=278+15-18\\ \Leftrightarrow3x=275\\ \Leftrightarrow x=\dfrac{275}{3}\\ ---\\ \left(7-x\right)\left(3x-90\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}7-x=0\\3x-90=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=30\end{matrix}\right.\)
Câu 4:
a) \(\left(1267-86\right)-\left(267+14\right)\)
\(=1267-86-267-14\)
\(=900\)
b) \(\left(3900-278\right)-\left(80-178\right)-520\)
\(=3900-278-80+178-520\)
\(=3200\)
c) \(\left(2023-79+15\right)-\left(-79+15\right)\)
\(=2023-79+15+79-15\)
\(=2023\)
d) \(-329-\left(15-101\right)-\left(25-101\right)\)
\(=-329-15+101-25+101\)
\(=-167\)
Câu 5:
Trong 2 bạn, không có ai là người trả lời đúng vì \(100-\left(37-49+12\right)=100-37+49-12\)
\(#WendyDang\)
a ) 128 . ( 278 - 302 ) + 278 . ( 302 - 128 )
= 128 . 278 - 128 . 302 + 278 . 302 - 128 . 278
= ( 128 . 278 - 128 . 278 ) + ( 278 . 302 - 128 . 302 )
= 302 . ( 278 - 128 )
= 302 . 100 = 30200 .
b ) 2 . ( - 7 )2 - 3 . ( - 4 )3 - 60
= 2 . 49 + 192 - 60
= 98 + 192 - 60
= 230 .