Tìm x: \(x\times4=16\div x\)
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29 tháng 5 2017
a) \(5\frac{8}{17}:x+\frac{-1}{17}:x+3\frac{1}{17}:17\frac{1}{3}=\frac{4}{17}\)
\(\frac{93}{17}:x+\frac{-1}{17}:x+\frac{52}{17}:\frac{52}{3}=\frac{4}{17}\)
\(\left(\frac{93}{17}+\frac{-1}{17}\right):x+\frac{52}{17}.\frac{3}{52}=\frac{4}{17}\)
\(\frac{92}{17}:x+\frac{3}{17}=\frac{4}{17}\)
\(\frac{92}{17}:x=\frac{4}{17}-\frac{3}{17}\)
\(\frac{92}{17}:x=\frac{1}{17}\)
\(x=\frac{92}{17}:\frac{1}{17}\)
\(x=92\)
b) \(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{x.\left(x+3\right)}=\frac{6}{19}\)
\(\frac{1}{3}.\left(1-\frac{1}{4}\right)+\frac{1}{3}.\left(\frac{1}{4}-\frac{1}{7}\right)+\frac{1}{3}.\left(\frac{1}{7}-\frac{1}{10}\right)+...+\frac{1}{3}.\left(\frac{1}{x}-\frac{1}{x+3}\right)=\frac{6}{19}\)
\(\frac{1}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{6}{19}\)
\(\frac{1}{3}.\left(1-\frac{1}{x+3}\right)=\frac{6}{19}\)
\(1-\frac{1}{x+3}=\frac{6}{19}:\frac{1}{3}\)
\(1-\frac{1}{x+3}=\frac{18}{19}\)
\(\frac{1}{x+3}=1-\frac{18}{19}\)
\(\frac{1}{x+3}=\frac{1}{19}\)
\(\Rightarrow x+3=19\)
\(\Rightarrow x=19-3\)
\(\Rightarrow x=16\)
17 tháng 12 2016
\(\frac{x+11}{12}+\frac{x+11}{13}+\frac{x+11}{14}=\frac{x+11}{15}+\frac{x+11}{16}\)
\(\Rightarrow\frac{x+11}{12}+\frac{x+11}{13}+\frac{x+11}{14}-\frac{x+11}{15}-\frac{x+11}{16}=0\)
\(\Rightarrow\left(x+11\right)\left(\frac{1}{12}+\frac{1}{13}+\frac{1}{14}-\frac{1}{15}-\frac{1}{16}\right)=0\)
Mà \(\left(\frac{1}{12}+\frac{1}{13}+\frac{1}{14}-\frac{1}{15}-\frac{1}{16}\right)\ne0\)
\(\Rightarrow x+11=0\Rightarrow x=-11\)
S
4
15 tháng 1 2017
\(x+x+x\times2+x\times4+x\times2=2016\)
\(x\times1+x\times1+x\times2+x\times4+x\times2=2016\)
\(x\times\left(1+1+2+4+2\right)=2016\)
\(x\times10=2016\)
\(x=2016\div10\)
\(x=201,6\)
17 tháng 7 2019
a) <=? |(x-1/4)| = 1/4-x
Th1: x >= 1/4 => x - 1/4 = 1/4 - x
<=> 2x = 2.1/4 <=> x = 1/4(nhân)
Th2: x<1/4 => -x + 1/4 = 1/4-x
<=> 0x = 0
<=> x thuộc R và x <1/4.
Vậy S ={x|x<=1/4}
17 tháng 7 2019
\(\text{a)}\sqrt{x^2-\frac{1}{2}x+\frac{1}{16}}=\frac{1}{4}-x\)
\(\Leftrightarrow\sqrt{x^2-2.x.\frac{1}{4}+\left(\frac{1}{4}\right)^2}=\frac{1}{4}-x\)
\(\Leftrightarrow\sqrt{\left(x-\frac{1}{4}\right)^2}=\frac{1}{4}-x\)
\(\Leftrightarrow x-\frac{1}{4}=\frac{1}{4}-x\)
\(\Leftrightarrow2x=\frac{1}{2}\)
\(\Leftrightarrow x=\frac{1}{4}\)
\(\text{b)}\sqrt{x-2\sqrt{x-1}}=\sqrt{x-1}-1\)
\(ĐKXĐ:x\ge-2\)
\(\Leftrightarrow\left(\sqrt{x-2\sqrt{x-1}}\right)^2=\left(\sqrt{x-1}-1\right)^2\)
\(\Leftrightarrow x-2\sqrt{x-1}=\left(\sqrt{x-1}\right)^2-2\sqrt{x-1}+1\)
\(\Leftrightarrow x-2\sqrt{x-1}=x-1-2\sqrt{x-1}+1\)
\(\Leftrightarrow x-2\sqrt{x-1}-x+2\sqrt{x-1}=-1+1\)
\(\Leftrightarrow0x=0\)
Vậy \(S=\left\{x\inℝ|x\ge-2\right\}\)
21 tháng 9 2020
A = ( x - 3 )3 - ( x + 1 )3 + 12x( x - 1 )
= x3 - 9x2 + 27x - 27 - ( x3 + 3x2 + 3x + 1 ) + 12x2 - 12x
= x3 - 9x2 + 27x - 27 - x3 - 3x2 - 3x - 1 + 12x2 - 12x
= ( x3 - x3 ) + ( 12x2 - 9x2 - 3x2 ) + ( 27x - 3x - 12x ) + ( -27 - 1 )
= 12x - 28
+)Với x = -2/3 => A = \(12\times\left(-\frac{2}{3}\right)-28=-8-28=-36\)
+) Để A = -16 => 12x - 28 = -16
=> 12x = 12
=> x = 1
21 tháng 9 2020
a) \(A=\left(x-3\right)^3-\left(x+1\right)^3+12x\left(x-1\right)\)
\(=\left(x^3-9x^2+27x-27\right)-\left(x^3+3x^2+3x+1\right)+\left(12x^2-12x\right)\)
\(=12x-28\)
b) Thay \(x=\frac{-2}{3}\)vào biểu thức A ta có:
\(A=12.\left(\frac{-2}{3}\right)-28=-36\)
Vậy giá trị của A là -36 tại x=-2/3
c) \(A=-16\Rightarrow12x-28=-16\)
\(\Leftrightarrow12x=-16+28\Leftrightarrow12x=12\Leftrightarrow x=1\)
Vậy để A=-16 thì x=1
\(x\times4=\frac{16}{x}\Rightarrow x\times x=\frac{16}{4}\Leftrightarrow x^2=4\Leftrightarrow x=\pm2\)
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