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1) ADTCDTSBN
có: \(\frac{x}{3}=\frac{y}{5}=\frac{z}{-7}=\frac{x-y-z}{3-5+7}=\frac{20}{5}=4.\)
=> ...
A=\(\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right).\left(\frac{1}{16}-1\right).............\left(\frac{1}{9801}-1\right).\left(\frac{1}{10000}-1\right)\)
A=\(\left(\frac{1-4}{4}\right).\left(\frac{1-9}{9}\right).\left(\frac{1-16}{16}\right).............\left(\frac{1-9801}{9801}\right).\left(\frac{1-10000}{10000}\right)\)
A=\(\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}.....................\frac{-9800}{9801}.\frac{-9999}{10000}\)
A=\(\frac{-1.3}{2^2}.\frac{-2.4}{3^2}.\frac{-3.5}{4^2}.....................\frac{-98.100}{99^2}.\frac{-99.101}{100^2}\)
A=\(\frac{\left[\left(-1\right).\left(-2\right).\left(-3\right)....................\left(-98\right).\left(-99\right)\right].\left(3.4.5............100.101\right)}{\left(2.3.4.........99.100\right).\left(2.3.4...............99.100\right)}\)
A=\(\frac{1.101}{100.2}\)=\(\frac{101}{200}\)
2
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.................+\frac{2}{x.\left(x+1\right)}=\frac{2015}{2017}\)
\(\frac{1}{3.2}+\frac{1}{6.2}+\frac{1}{10.2}+.................+\frac{2}{2.x.\left(x+1\right)}=\frac{1}{2}.\frac{2015}{2017}\)
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+.................+\frac{1}{x.\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}\)
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+..................+\frac{1}{x.\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+..............+\frac{1}{x}-\frac{1}{x+1}=\frac{2015}{2017}.\frac{1}{2}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2015}{2017}.\frac{1}{2}\)
\(\frac{x+1}{2.\left(x+1\right)}-\frac{2}{2.\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}\)
\(\frac{\left(x+1\right)-2}{2.\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}\)
\(\frac{x-1}{2.\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}\)
=>\(\frac{x-1}{x+1}=\frac{2015}{2017}.\frac{1}{2}:\frac{1}{2}\)
\(\frac{x-1}{x+1}=\frac{2015}{2017}\)
=>x+1=2017
=>x=2018-1
=>x=2016
Vậy x=2016
Còn bài 3 em ko biết làm em ms lớp 6
Chúc anh học tốt
a ) 4x+2 +4x+1 = 1040
4x.42+4x.4=1040
4x.(42+4)=1040
4x.(16+4)=1040
4x.20=1040
4x=1040:20
4x=52
Vô lí vì 52 ko chuyển thành 4 mũ mấy đc
Vậy \(x\in\varnothing\)
\(b)\left(x-\sqrt{3}\right)^2=\frac{3}{4}\)
Vô lí vì \(\frac{3}{4}\)ko chuyển thành đc mũ 2
Vậy \(x\in\varnothing\)
Mình sẽ giúp bạn làm câu còn lại :)))
\(\left(x-\sqrt{3}\right)^2=\frac{3}{4}\)
\(\Leftrightarrow x-\sqrt{3}=\pm\sqrt{\frac{3}{4}}\)
\(\Leftrightarrow x-\sqrt{3}=\pm\frac{\sqrt{3}}{2}\)
\(\Leftrightarrow\orbr{\begin{cases}x-\sqrt{3}=\frac{\sqrt{3}}{2}\\x-\sqrt{3}=-\frac{\sqrt{3}}{2}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{3\sqrt{3}}{2}\\x=\frac{\sqrt{3}}{2}\end{cases}}\)
\(f\left(x\right)-g\left(x\right)=5x^2-2x+5-\left(5x^2-6x-\frac{1}{3}\right)\)
= \(5x^2-2x+5-5x^2+6x+\frac{1}{3}\)
=\(4x+\frac{16}{3}\)
\(x^{2017}=\frac{x^{2017}-2}{3}\)
\(\Leftrightarrow x^{2017}=\frac{x^{2017}-2}{3}-\frac{x^{2017}-2}{3}\)
\(\Leftrightarrow\frac{2x^{2017}+2}{3}=0\)
\(\Leftrightarrow2x^{2017}+2=0.3\)
\(\Leftrightarrow2x^{2017}+2=0\)
\(\Leftrightarrow2x^{2017}=0-2\)
\(\Leftrightarrow2x^{2017}=-2\)
\(\Leftrightarrow x^{2017}=-2:2\)
\(\Leftrightarrow x^{2017}=-1\)
\(\Leftrightarrow x=\left(-1\right)^{\frac{1}{2017}}\)
=> x = -1
Lần này cẩn thận hơn rồi nha :v
-1
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