3.x+(-42)=2.(x+1)+(-58)
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a) 1 267 + 99 + 501 = 1 267 + (99 + 501)
= 1 267 + 600 = 1 867
25 x 14 x 4 = (25 x 4) x 14
= 100 x 14 = 1 400
b) 3 905 x (50 – 1) = 3 905 x 50 – 3 905 x 1
= 195 250 – 3 905 = 191 345
270 : ( 27 x 2 ) = 270 : 27 : 2
= 10 : 2 = 5
c) 115 x 58 + 115 x 42 = 115 x (58 + 42)
= 115 x 100 = 11 500
136 x 67 – 136 x 66 = 136 x (67 – 66)
= 136 x 1 = 136
`@` `\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`
2: =>2x^2-8x+4=x^2-4x+4 và x>=2
=>x^2-4x=0 và x>=2
=>x=4
3: \(\sqrt{x^2+x-12}=8-x\)
=>x<=8 và x^2+x-12=x^2-16x+64
=>x<=8 và x-12=-16x+64
=>17x=76 và x<=8
=>x=76/17
4: \(\sqrt{x^2-3x-2}=\sqrt{x-3}\)
=>x^2-3x-2=x-3 và x>=3
=>x^2-4x+1=0 và x>=3
=>\(x=2+\sqrt{3}\)
6:
=>\(\sqrt{\left(\sqrt{x-1}+1\right)^2}-\sqrt{\left(\sqrt{x-1}-1\right)^2}=-2\)
=>\(\sqrt{x-1}+1-\left|\sqrt{x-1}-1\right|=-2\)
=>\(\left|\sqrt{x-1}-1\right|=\sqrt{x-1}+1+2=\sqrt{x-1}+3\)
=>1-căn x-1=căn x-1+3 hoặc căn x-1-1=căn x-1+3(loại)
=>-2*căn x-1=2
=>căn x-1=-1(loại)
=>PTVN
1) ĐK: \(x\ge\dfrac{5}{2}\)
pt <=> \(x-4=\sqrt{2x-5}\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge4\\\left(x-4\right)^2=2x-5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge4\\x^2-8x+16=2x-5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge4\\x^2-10x+21=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge4\\\left(x-3\right)\left(x-7\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge4\\\left[{}\begin{matrix}x=3\left(l\right)\\x=7\left(n\right)\end{matrix}\right.\end{matrix}\right.\)
Vậy, pt có nghiệm duy nhất là x=7
2) ĐK: \(2x^2-8x+4\ge0\)
pt <=> \(\left\{{}\begin{matrix}x\ge2\\2x^2-8x+4=x^2-4x+4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\x^2-4x=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\x\left(x-4\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\\left[{}\begin{matrix}x=0\left(l\right)\\x=4\left(n\right)\end{matrix}\right.\end{matrix}\right.\)
Vậy, pt có nghiệm duy nhất là x=4
3) ĐK: \(x\ge3\)
pt <=> \(\left\{{}\begin{matrix}x\le8\\x^2+x-12=x^2-16x+64\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\le8\\17x=76\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\le8\\x=\dfrac{76}{17}\left(n\right)\end{matrix}\right.\)
Vậy, pt có nghiệm duy nhất là \(x=\dfrac{76}{17}\)\(\)
(100+42) x42+(200-58)x58
=142x42+142x58
=142x(42+58)
=142x100
=14200
\(\left(100+42\right)\times42+\left(200-58\right)\times58\)
\(=142\times42+142\times58\)
\(=142\times\left(42+58\right)\)
\(=142\times100=14200\)
(100 + 42 ) x 42 + ( 200 - 58 ) x 58
= 142 x 42 + 142 x 58
= 142 x ( 42 + 58 )
= 142 x 100
= 14200
( 100 + 42 ) x 42 + ( 200 - 58 ) x 58
= 142 x 42 + 142 x 58
= 142 x ( 42 + 58 )
= 142 x 100
= 14200
a. 64 x 25 + 35 x 25 + 25
= 64 x 25 + 35 x 25 + 25 x 1
= 25 x ( 64 + 35 + 1 )
= 25 x 100
= 2500
b. 58 x 42 + 32 x 8 + 5 x 16
c. ( 42 x 43 + 57 x 43 + 43 ) - 360 : 4
= 42 x 43 + 57 x 43 + 43 x 1 - 90
= 43 x ( 42 + 57 +1 ) - 90
= 43 x 100 - 90
= 4300 - 90
= 4210
d. 456 : 2 x 181456 : 3 - 102
Trả lời:
a,\(64\times25+35\times25+25\)
\(=25\times\left(64+35+1\right)\)
\(=25\times100\)
\(=2500\)
b,\(58\times42+32\times8+5\times16\)
\(=2436+256+80\)
\(=2772\)
c,\(\left(42\times43+57\times43+43\right)-360\div4\)
\(=43\times\left(42+57+1\right)-90\)
\(=43\times100-90\)
\(=4300-90\)
\(=4210\)
d,\(456\div2\times181456\div3-102\)
\(=228\div3\times181456-102\)
\(=76\times181456-102\)
\(=13790656-102\)
\(=13790554\)
58 x 42 + 32 x 8 + 5 x 16
= 58 x 42 + 32 x 8 + 5 x 2 x 8
= 58 x42 + 32 x 8 + 10 x 8
= 58 x 42 + ( 32 + 10 ) x 8
= 58 x 42 + 42 x 8
= 42 x ( 58 + 8 )
= 42 x 66
= 2772
3.x+(-42)=2.(x+1)+(-58)
=> 3x-42=2x+2-58
=> 3x-42=2x-56
=> 3x-2x=-56+42
=> x=-14