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#)Giải :
a) x + 2x + 3x + ... + 100x = - 213
=> 100x + ( 2 + 3 + 4 + ... + 100 ) = - 213
=> 100x + 5049 = - 213
<=> 100x = - 5262
<=> x = - 52,62
#)Giải :
b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}x-\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{3}+\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{2}\)
\(\Rightarrow\left(\frac{1}{2}+\frac{1}{4}\right)x=\frac{1}{2}\)
\(\Rightarrow\frac{3}{4}x=\frac{1}{2}\)
\(\Leftrightarrow x=\frac{2}{3}\)
\(\left(\frac{1}{2}\right)^5\times x=\left(\frac{1}{2}\right)^7\)
\(x=\left(\frac{1}{2}\right)^7\div\left(\frac{1}{2}\right)^5\)
\(x=\left(\frac{1}{2}\right)^{7-5}=\left(\frac{1}{2}\right)^2=\frac{1}{4}\) .
\(\left(\frac{3}{7}\right)^2\times x=\left(\frac{9}{21}\right)^2\)
\(\left(\frac{3}{7}\right)^2\times x=\left(\frac{3}{7}\right)^4\)
\(x=\left(\frac{3}{7}\right)^4\div\left(\frac{3}{7}\right)^2\)
\(x=\left(\frac{3}{7}\right)^{4-2}=\left(\frac{3}{7}\right)^2=\frac{9}{49}\)
\(2^x=2\Rightarrow x=1\)
\(3^x=3^4\Rightarrow x=4\)
\(7^x=7^7\Rightarrow x=7\)
\(\left(-3\right)^x=\left(-3\right)^5\Rightarrow x=5\)
\(\left(-5\right)^x=\left(-5\right)^4\Rightarrow x=4\)
\(2^x=4\Leftrightarrow2^x=2^2\Rightarrow x=2\)
\(2^x=8\Leftrightarrow2^x=2^3\Rightarrow x=3\)
\(2^x=16\Leftrightarrow2^x=2^4\Rightarrow x=4\)
\(3^{x+1}=3^2\Leftrightarrow x+1=2\Leftrightarrow x=2-1\Rightarrow x=1\)
\(5^{x-1}=5\Leftrightarrow x-1=1\Leftrightarrow x=1+1\Rightarrow x=2\)
\(6^{x+4}=6^{10}\Leftrightarrow x+4=10\Leftrightarrow x=10-4\Rightarrow x=6\)
\(5^{2x-7}=5^{11}\Leftrightarrow2x-7=11\Leftrightarrow2x=11+7\Leftrightarrow2x=18\Leftrightarrow x=18\div2\Rightarrow x=9\)
\(\left(-2\right)^{4x+2}=64\)
\(2^{-4x+2}=2^6\Leftrightarrow-4x+2=6\Leftrightarrow-4x=6-2\Leftrightarrow-4x=4\Leftrightarrow x=4\div\left(-4\right)\Rightarrow x=-1\)
\(\left(\frac{1}{2}\right)^x=\left(\frac{1}{2}\right)^5\Rightarrow x=5\)
\(\left(\frac{5}{6}\right)^{2x}=\left(\frac{5}{6}\right)^5\Rightarrow2x=5\Rightarrow x=\frac{5}{2}\)
\(\left(\frac{3}{4}\right)^{2x-1}=\left(\frac{3}{4}\right)^{5x-4}\Rightarrow2x-1=5x-4\)
\(2x-5x=-4+1\)
\(-3x=-3\Rightarrow x=1\)
\(\left(\frac{-1}{10}\right)^x=\frac{1}{100}\)
\(\left(\frac{1}{10}\right)^{-x}=\left(\frac{1}{10}\right)^2\Rightarrow-x=2\Rightarrow x=-2\)
\(\left(\frac{-3}{2}\right)^x=\frac{9}{4}\)
\(\left(\frac{3}{2}\right)^{-x}=\left(\frac{3}{2}\right)^2\Rightarrow-x=2\Rightarrow x=-2\)
\(\left(\frac{-3}{5}\right)^{2x}=\frac{9}{25}\)
\(\left(\frac{3}{5}\right)^{-2x}=\left(\frac{3}{5}\right)^2\Rightarrow-2x=2\Rightarrow x=-1\)
\(\left(\frac{-2}{3}\right)^x=\frac{-8}{27}\)
\(\left(\frac{-2}{3}\right)^x=\left(\frac{-2}{3}\right)^3\Rightarrow x=3\).
hehe.
đánh tới què tay, hoa mắt lun r nekkk!!
\(\left(4x+3\right)^2=\frac{2}{3}:6\)
\(\left(4x+3\right)^2=\frac{1}{9}\)
\(\left(4x+3\right)^2=\left(\frac{1}{3}\right)^2\)
\(\Rightarrow4x+3=\frac{1}{3}\)
\(4x=-\frac{8}{3}\)
\(x=-\frac{2}{3}\)
a)\(\frac{3x+2}{7}=\frac{4x-5}{6}\)
\(\Leftrightarrow\frac{6\left(3x+2\right)}{42}=\frac{7\left(4x-5\right)}{42}\)
\(\Leftrightarrow6\left(3x+2\right)=7\left(4x-5\right)\)
\(\Leftrightarrow18x+12=28x-35\)
\(\Leftrightarrow18x-28x=-12-35\)
\(\Leftrightarrow-10x=-47\Leftrightarrow x=\frac{47}{10}\)
b) \(\frac{x+1}{x+3}=\frac{x+2}{x+4}\left(đkxđ:x\ne-3,-4\right)\)
\(\Leftrightarrow\frac{\left(x+1\right)\left(x+4\right)}{\left(x+3\right)\left(x+4\right)}=\frac{\left(x+2\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}\)
\(\Leftrightarrow\left(x+1\right)\left(x+4\right)=\left(x+2\right)\left(x+3\right)\)
\(\Leftrightarrow\left(x+1\right)\left(x+4\right)-\left(x+2\right)\left(x+3\right)=0\)
\(\Leftrightarrow x^2+4x+x+4-x^2-3x+2x+6=0\)
\(\Leftrightarrow\left(x^2-x^2\right)+\left(4x+4\right)+\left(4+6\right)+\left(x-3x\right)=0\)
\(\Leftrightarrow4x+4+10-2x=0\)
\(\Leftrightarrow4x+14-2x=0\)
\(\Leftrightarrow2x=-14\Leftrightarrow x=-7\)
a) \(\frac{3x+2}{7}=\frac{4x-5}{6}\)
=> \(6\left(3x+2\right)=7\left(4x-5\right)\)
=> \(18x+12=28x-35\)
=> \(18x+12-28x+35=0\)
=> \(\left(18x-28x\right)+\left(12+35\right)=0\)
=> \(-10x+47=0\)
=> \(-10x=-47\Rightarrow x=\frac{47}{10}\)
b) \(\frac{x+1}{x+3}=\frac{x+2}{x+4}\)
=> (x + 1)(x + 4) = (x + 2)(x + 3)
=> x(x + 4) + 1(x + 4) = x(x + 3) + 2(x + 3)
=> x2 + 4x + x + 4 = x2 + 3x + 2x + 6
=> x2 + 5x + 4 = x2 + 5x +6
=> x2 + 5x + 4 - x2 - 5x - 6 = 0
=> (x2 - x2) + (5x - 5x) + (4 - 6) = 0
=> -2 \(\ne\)0
=> không tìm được x thỏa mãn
hay cách khác : \(\frac{x+1}{x+3}=\frac{x+2}{x+4}\)
=> \(\frac{x+3-2}{x+3}=\frac{x+4-2}{x+4}\)
=> \(1-\frac{2}{x+3}=1-\frac{2}{x+4}\)
=> \(1-\frac{2}{x+3}-\left(1-\frac{2}{x+4}\right)=0\)
=> \(1-\frac{2}{x+3}-1+\frac{2}{x+4}=0\)
=> \(\left(1-1\right)+\left(-\frac{2}{x+3}+\frac{2}{x+4}\right)=0\)
=> \(-\frac{2}{x+3}+\frac{2}{x+4}=0\)
=> \(\frac{-2\left(x+4\right)+2\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}=0\)
=> \(-2x-8+2x+6=0\)
=> \(\left(-2x+2x\right)+\left(-8+6\right)=0\)
=> \(-2\ne0\)
=> không tìm được x thỏa mãn
a, ( 152 +và 2/4 - 148 và 3/8 ) : 0,2 = x : 0,3
=> 33/8 : 1/5 = x : 3/10
=> x : 3/10 = 165/8
=> x = 99/10
b, ( 85 và 7/30 - 83 và 5/18 ) : 2 và 2/3 = 0,01x : 4
=> 88/45 : 8/3 = 0,01x : 4
=> 0,01x : 4 = 11/15
=> 0,01x = 44/15
=> x = 880/3
c, x - 1/ x + 5 = 6/7
=> 7( x - 1 ) = 6( x + 5 )
=> 7x - 7 = 6x + 30
=> 7x - 6x = 7 + 30
=> x = 37
d, x2/6 = 24/25
=> x2. 25 = 6 . 24
=> x2.25 = 144
=> x2 = 144/25
=> x = ( 12/5)2 hoặc x = ( -12/5)
g, x - 3/ x + 5 = 5/7
=> 7( x - 3 ) = 5 ( x + 5 )
=> 7x - 21 = 5x + 25
=> 7x - 5x = 21 + 25
=> 2x = 46
=> x = 23