Tìm x,biết:
3(x+6)-53=2(x-8)-1
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Ta có : \(x^2+3x+2=x^2-2x+1+5x-5+6\)
\(=\left(x-1\right)^2+5\left(x-1\right)+6\)
Ta có: \(P=\dfrac{x^2+\sqrt{x}}{x-\sqrt{x}+1}-\dfrac{2\left(x+\sqrt{x}\right)}{\sqrt{x}}+\dfrac{2\left(x-1\right)}{\sqrt{x}-1}\)
\(=x+\sqrt{x}-2\left(\sqrt{x}+1\right)+2\left(\sqrt{x}+1\right)\)
\(=x+\sqrt{x}\)
Thay x=-1 vào pt, ta được:
\(2m-1+2=m+3\)
=>2m+1=m+3
hay m=2
a)\(\frac{x}{5}=\frac{2}{5}\)
\(\Leftrightarrow x=\frac{2\times5}{5}=2\)
Vậy .............
b) \(\frac{3}{8}=\frac{6}{x}\)
\(\Leftrightarrow x=\frac{8\times6}{3}=16\)
Vậy ................
c) \(\frac{1}{9}=\frac{x}{27}\)
\(\Leftrightarrow x=\frac{1\times27}{9}=3\)
Vậy ................
d) \(\frac{4}{x}=\frac{8}{6}\)
\(\Leftrightarrow x=\frac{4\times6}{8}=3\)
Vậy ............
e) \(\frac{3}{x-5}=\frac{-4}{x+2}\)
\(\Leftrightarrow3\left(x+2\right)=-4\left(x-5\right)\)
\(\Leftrightarrow3x+6=-4x+20\)
\(\Leftrightarrow3x+4x=20-6\)
\(\Leftrightarrow7x=14\)
\(\Leftrightarrow x=2\)
Vậy .............
f) \(\frac{x}{-2}=\frac{-8}{x}\)
\(\Leftrightarrow x^2=16\)
\(\Leftrightarrow x=\pm4\)
Vậy ...............
\(\frac{x}{5}=\frac{2}{5}\Rightarrow x=\frac{2\times5}{5}=2\)
\(\frac{1}{9}=\frac{x}{27}\Rightarrow x=\frac{1\times27}{9}=3\)
\(\frac{4}{x}=\frac{8}{6}\Rightarrow x=\frac{8\times6}{8}=6\)
\(\frac{3}{x-5}=\frac{-4}{x+2}\)
\(\Rightarrow3.\left(x+2\right)=-4.\left(x-5\right)\)
\(\Rightarrow3x+6=-4x+20\)
\(\Rightarrow3x+4x=20-6\)
\(\Rightarrow7x=14\)
\(\Rightarrow x=2\)
\(=\dfrac{x^2+x-x^2+x+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{2x+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{2}{x-1}\)
Bài 2:
Ta có: (x-3)(x+4)>0
=>x>3 hoặc x<-4
Bài 3:
a: \(5S=5-5^2+...+5^{99}-5^{100}\)
\(\Leftrightarrow6S=1-5^{100}\)
hay \(S=\dfrac{1-5^{100}}{6}\)
\(8x-48+4x-12-14=-x+4\)
\(\Leftrightarrow12x-75=-x+4\Leftrightarrow13x=79\Leftrightarrow x=\dfrac{79}{13}\)
\(-7\left(8-x\right)-6\left(x+9\right)=20-x\Leftrightarrow-56+7x-6x-54=20-x\)
\(\Leftrightarrow2x=130\Leftrightarrow x=65\)
\(9x-63-80+60x=-7x+15\Leftrightarrow76x=158\Leftrightarrow x=\dfrac{79}{38}\)
\(-96-16x-60+30x=-40x-16\Leftrightarrow54x=140\Leftrightarrow x=\dfrac{70}{27}\)
\(17x-102-14x-28=4x-24-2x+4\Leftrightarrow x=110\)
\(\Leftrightarrow2A=2+2^2+2^3+...+2^{2022}\\ \Leftrightarrow2A-A=2+2^2+...+2^{2022}-1-2-2^2-...-2^{2021}\\ \Leftrightarrow A=2^{2022}-1\\ \Leftrightarrow A+1=2^{2022}\)
Mà \(A+1=2^x\Leftrightarrow x=2022\)
TK :
978 : ( 7 × x - 18 ) - 216 = 2 + 4 + 6 + ..... + 20
978 : ( 7 × x - 18 ) - 216 = (20 + 2) x [ (20 - 2) : 2 + 1] : 2
978 : ( 7 × x - 18 ) - 216 = 22 x [ 18 : 2 + 1] : 2
978 : ( 7 × x - 18 ) - 216 = 22 x [ 9 + 1] : 2
978 : ( 7 × x - 18 ) - 216 = 22 x 10 :2
978 : ( 7 × x - 18 ) - 216 = 220 : 2
978 : ( 7 × x - 18 ) - 216 = 110
978 : ( 7 × x - 18 ) = 110 + 216
978 : ( 7 × x - 18 ) = 326
7 × x - 18 = 978 : 326
7 × x - 18 = 3
7 × x = 3 + 18
7 × x = 21
x = 21 : 7
x = 3
ta có : `2 + 4 + 6 + ..... + 20`
số số hạng là : `(20-2):2+1= 10`
tổng là : `(20+2) xx 10 :2=110`
`978 : ( 7 × x - 18 ) - 216 = 2 + 4 + 6 + ..... + 20`
`978 : ( 7 × x - 18 ) - 216 =110`
`978 : ( 7 × x - 18 )=110+216`
`978 : ( 7 × x - 18 )=326`
`7 × x - 18=978 :326`
`7 × x - 18=3`
`7 xx x=3+18`
`7 xx x=21`
`x=21:7`
`x=3`
vậy `x=3`