2^x+253=y^2
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`B=(x-x/(x+1))-(1-x/(x+1))`
`đkxđ:x ne +-1`
`=((x^2+x-x)/(x+1))-(x+1-x)/(x+1)`
`=x^2/(x+1)-1/(x+1)`
`=(x^2-1)/(x+1)`
`=((x-1)(x+1))/(x+1)`
`=x-1`
`2)(x-1)^2-25`
`=(x-1)^2-5^2`
`=(x-1-5)(x-1+5)`
`=(x-6)(x+4)`
Bài 1:
Ta có: \(B=\left(x-\dfrac{x}{x+1}\right)-\left(1-\dfrac{x}{x+1}\right)\)
\(=\left(\dfrac{x\left(x+1\right)-x}{x+1}\right)-\left(\dfrac{x+1-x}{x+1}\right)\)
\(=\dfrac{x^2+x-x-\left(x+1-x\right)}{x+1}\)
\(=\dfrac{x^2-1}{x+1}=x-1\)
a) \(2\times x+3\times x=\frac{5}{2}\)
=> \(\left(2+3\right)\times x=\frac{5}{2}\)
=> \(5\times x=\frac{5}{2}\)
=> \(x=\frac{5}{2}:5=\frac{5}{2}\times\frac{1}{5}=\frac{1}{2}\)
b) \(145+x\times12-432=253\)
=> \(145+x\times12=253+432\)
=> \(145+x\times12=685\)
=> \(x\times12=685-145\)
=> \(x\times12=540\Rightarrow x=45\)
Câu a) 2 x X + 3 x X = 5/2
( 2+3 ) x X = 5/2
5 x X = 5/2
X =5/2 : 5
X = 1/2
Câu b) 145 + X x 12 - 432 = 253
145 + X x 12 = 253 + 432
145 + X x 12 = 685
X x 12 = 685 - 145
X x 12 = 540
X = 540 : 12
X = 45
1) \(x^2y+x\left(2y-1\right)=7\)
\(\Leftrightarrow x^2y+2xy-x=7\)
\(\Leftrightarrow xy\left(x+2\right)-x-2=7-2\)
\(\Leftrightarrow xy\left(x+2\right)-\left(x+2\right)=5\)
\(\Leftrightarrow\left(xy-1\right)\left(x+2\right)=5\)
\(\Rightarrow\)xy - 1 và x + 2 là ước của 5 là \(\pm1;\pm5\)
đến đây tự lm đc
2 ) \(B=\frac{255}{1}+\frac{254}{2}+\frac{253}{3}+....+\frac{3}{253}+\frac{2}{254}+\frac{1}{255}\)
\(=\left(\frac{254}{2}+1\right)+\left(\frac{253}{3}+1\right)+....+\left(\frac{2}{254}+1\right)+\left(\frac{1}{255}+1\right)+1\)
\(=\frac{256}{2}+\frac{256}{3}+....+\frac{256}{255}+\frac{256}{256}\)
\(=256\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{255}+\frac{1}{256}\right)=256A\)
\(\Rightarrow\frac{B}{A}=256=16^2\) Là số CP (đpcm)
\(a,250:\left(10-x\right)=25\\ \Rightarrow10-x=250:25\\ \Rightarrow10-x=10\\ \Rightarrow x=10-10=0\\ b,3x-2018:2=23\\ \Rightarrow3x-1009=23\\ \Rightarrow3x=23+1009\\ \Rightarrow3x=1032\\ \Rightarrow x=1032:3=344\\ c,\left(9x-21\right):3=2\\ \Rightarrow9x-21=2\times3\\ \Rightarrow9x-21=6\\ \Rightarrow9x=21+6\\ \Rightarrow9x=27\\ \Rightarrow x=27:9=3\)
\(d,53\left(9-x\right)=53\\ \Rightarrow9-x=53:53\\ \Rightarrow9-x=1\\ \Rightarrow x=9-1=8\)