(x+1)+(x+2)=+........+(x+6)=78
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a) 2 x 12 x 43 + 3 x 32 x 8 + 25 x 6 x4
=(2 x12) x43+(3 x8) x32+(6 x4) x25
=24 x43+24 x32+ 24 x25
=24 x(43+32+25)
=24 x100
=2400
b) 78 x 31 + 78 x 24 + 17 x 78 + 28 x 78
=78x(31+24+17+28)
=78x100
=7800
Lời giải:
a.
$23+23\times 45+23\times 44=23\times (1+45+44)=23\times 90$
$=23\times (100-10)=23\times 100-23\times 10=2300-230=2070$
b.
$=36\times 280-36\times 79-36$
$=36\times (280-79-1)=36\times (280-80)=36\times 200=7200$
c.
$=72\times 10+72\times 25+72\times 66-72$
$=72\times (10+25+66-1)=72\times 100=7200$
`@` `\text {Ans}`
`\downarrow`
`23 + 23 \times 45 + 23 \times 44`
`= 23 \times (1+45 + 44)`
`= 23 \times 90`
`= 2070`
`b)`
`36 \times 280 - 9 \times 79 \times 4 - 36`
`= 36 \times 280 - 9 \times 4 \times 79 - 36`
`= 36 \times 280 - 36 \times 79 - 36`
`= 36 \times (280 - 79 - 1)`
`= 36 \times 200`
`= 7200`
`c)`
`8 \times 9 \times 10 + 6 \times 25 \times 12 + 4 \times 18 \times 66 - 2 \times 36`
`= 2 \times 4 \times 9 \times 10 + 6 \times 2 \times 6 \times 25 + 2 \times 2 \times 18 \times 66 - 2 \times 36`
`= 10 \times 2 \times 36 + 36 \times 2 \times 25 + 36 \times 2 \times 66 - 2 \times 36`
`= 36 \times 2 \times (10 + 25 + 66 - 1)`
`= 72 \times 100`
`= 7200`
_____
`c)`
`439 \times 78 - 38 \times 78 - 78`
`= 78 \times (439 - 38 - 1)`
`= 78 \times 400`
`= 31200`
`d)`
`24 \times 13 + 6 \times 89 \times 4 - 2 \times 24`
`= 24 \times 13 + 24 \times 89 - 2 \times 24`
`= 24 \times (13 + 89 - 2)`
`= 24 \times 100`
`= 2400`
`@` `\text {Ans}`
`\downarrow`
`2023 \times 14 + 2023 \times 83+97`
`= 2023 \times (14+83) + 97`
`= 2023 \times 97 + 97`
`= 196231 +97`
`= 196328`
`78 \times 31+78 \times 24+78 \times 17+78 \times 22 \times 72`
`= 78 \times (31+24+17+22 \times 72)`
`= 78 \times (31+24+17+1584)`
`= 78 \times 1656`
`= 129168`
`371 \times 69+371 \times 14+629 \times 83`
`= 371 \times (69+14) + 629 \times 83`
`= 371 \times 83 + 629 \times 83`
`= 83 \times (371+629)`
`= 83 \times 1000`
`= 83000`
`91 \times 51+49 \times 163-49 \times 72`
`= 91 \times 51 + 49 \times (163-72)`
`= 91 \times 51+49 \times 91`
`= 91 \times (51+49)`
`= 91 \times 100`
`= 9100`
`3 \times 12 \times 17 + 4 \times 9 \times 81 + 2 \times 6 \times 6`
`= 9 \times 4 \times 17 + 4 \times 9 \times 81 + 4 \times 9 \times 2`
`= 9 \times 4 \times (17+81+2)`
`= 36 \times 100`
`= 3600`
`42 \times 17 + 58 \times 83 \times 42 \times 83 + 42 \times 83 + 17`
`= 17 \times (42+58) + 42 \times 83 \times (58 \times 83 +1)`
`= 17 \times 100 + 3486 \times 4815`
`= 1700 + 16785090`
`= 16786790`
Ta có:\(\left(x-4\right)\left(x-1\right)^2=0\)
\(\Leftrightarrow x-4=0\) hoặc \(\left(x-1\right)^2=0\)
\(\Leftrightarrow x=4\) hoặc \(x-1=0\)
\(\Leftrightarrow x=4\) hoặc x=1
\(\left(2x-6\right)\left(x^2+1\right)=0\)
\(\Leftrightarrow2x-6=0\) hoặc \(x^2+1=0\)(vô lí)
\(\Leftrightarrow2x=6\)
\(\Leftrightarrow x=3\)
Xét VT ta có:1+2+3+4+...+x=\(\frac{x\left(x+1\right)}{2}\)
Mà VP=78
\(\Rightarrow\frac{x\left(x+1\right)}{2}=78\)
\(\Rightarrow x\left(x+1\right)=156\)
\(x\left(x+1\right)=12\cdot13\)
\(\Rightarrow x=12\)
A = 78 x 31 + 78 x 24 + 78 x 17 + 22 x 72
A = 78 x ( 31 + 24 + 17 ) + 22 x 72
A = 78 x 72 + 22 x 72
A = 72 x ( 78 + 22 )
A = 72 x 100
A = 7200
C = 53 x 39 + 47 x 39 - 53 x 21 - 47 x 21
C = 39 x ( 53 + 47 ) - 21 x ( 53 - 47 )
C = 39 x 100 - 21 x 6
C = 3900 - 126
C = 3774
Đề là : (x + 1) + (x + 2) + .... + (x + 6) = 78
=> 6x + ( 1 + 2 + 3 + 4 + 5 + 6 ) = 78
=> 6x + 21 = 78
=> 6x = 57
=> x = 57 : 6
=> x = \(\frac{19}{2}=9,5\)