\(x^2=\)\(\frac{19}{2}\)
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Ê hỗn số \(1\frac{19}{19}\)là sai vì 19 vẫn chia típ đc cho 19
\(2+\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x\left(x+1\right)}=2\)
\(\Rightarrow2\left(1+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=2-\frac{2}{3}\)
\(\Rightarrow2\left(1+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}+\frac{1}{x+1}\right)=\frac{4}{3}\)
\(\Rightarrow2\left(1+\frac{1}{2}-\frac{1}{x+1}\right)=\frac{4}{3}\)
\(\Rightarrow3+\frac{1}{x+1}=\frac{4}{3}\)
\(\Rightarrow\frac{1}{x+1}=\frac{4}{3}-3\)
\(\Rightarrow\frac{1}{x+1}=\frac{-5}{3}\)
\(\Rightarrow x=\frac{-8}{5}\)
Mà \(x\in N\Rightarrow\)đề sai :D
\(-\frac{5}{6}x-1\frac{13}{19}:3\frac{7}{19}-\left(-0,12\right)=\left(-\frac{1}{2}\right)^2\)
\(\Rightarrow-\frac{5}{6}x-\frac{32}{19}:\frac{64}{19}+0,12=\frac{1}{4}\)
\(\Rightarrow-\frac{5}{6}x-\frac{1}{2}=\frac{1}{4}-0,12=\frac{13}{100}\)
\(\Rightarrow-\frac{5}{6}x=\frac{63}{100}\)
\(\Rightarrow x=-\frac{189}{250}\)
-5/6x-32/19:64/19+3/25=1/4
-5/6x-32/19×19/64+3/25=1/4
-5/6x-1/2+3/25=1/4
-5/6x-31/50=1/4
-5/6x=1/4+31/50
-5/6x=87/100
x=87/100:-5/6
x=87/100×-6/5
x=-261/250
vậy x=-261/250
C1) 17/25.13/19+17/25.6/19 C2) 17/25.13/19+17/25.6/19
=17/25.(13/19+6/19) =221/475+102/475
=17/25.1=17/25 =17/25
Học tốt nha
\(C1:\)
\(\frac{17}{25}x\frac{13}{19}+\frac{17}{25}x\frac{6}{19}\)
\(=\frac{17}{25}x\left(\frac{13}{19}+\frac{6}{19}\right)\)
\(=\frac{17}{25}x1\)
\(=\frac{17}{25}\)
\(C2:\)
\(\frac{17}{25}x\frac{13}{19}+\frac{17}{25}x\frac{6}{19}\)
\(=\frac{221}{475}+\frac{102}{475}\)
\(=\frac{323}{475}=\frac{17}{25}\)
ĐKXĐ: ...
\(\Leftrightarrow\frac{x^2+x+1}{x^2+2x+1}-\frac{3}{4}+\frac{x^2+3x+1}{x^2+4x+1}-\frac{5}{6}=0\)
\(\Leftrightarrow\frac{x^2-2x+1}{4\left(x^2+2x+1\right)}+\frac{x^2-2x+1}{6\left(x^2+4x+1\right)}=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-2x+1=0\\4\left(x^2+2x+1\right)=6\left(x^2+4x+1\right)\end{matrix}\right.\)
\(\Leftrightarrow...\)
Ta có : \(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)642-\left[0,04:\left(x+1,05\right)\right]:0,12=19\)
=> \(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)642-0,04:\left(x+1,05\right):0,12=19\)
=>
(nãy bấm nhầm) tiếp nà :
=> \(\left(\frac{1}{11}-\frac{1}{21}\right)462-0,04:\left(x+1,05\right):0,12=19\)
=> \(\frac{10}{231}.462-0,04:\left(x+1,05\right):0,12=19\)
=> \(20-0,04:\left(x+1,05\right):0,12=19\)
=> 0,04 : (x + 1,05) : 0,12 = 1
=> 0,04 : (x + 1,05) = 0,12
=> \(x+1,05=\frac{1}{3}\)
=> \(x=\frac{1}{3}-1,05=...\)
1 : 29 x ( 19 -13 ) - 19 x ( 29 - 13 )
= 29 x 6 - 19 x 16
= 174 - 304
= - 130
2 : 1 - \(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
= 1 - \(\frac{1}{100}\)
= \(\frac{99}{100}\)
\(x^2=\frac{19}{2}\)suy ra \(x=\sqrt{\frac{19}{2}}\)
\(x^2=\frac{19}{2}\Rightarrow x=\pm\frac{\sqrt{19}}{\sqrt{2}}\)