( X - 1/2 ) . 5/2 + 1/2 = 7/4

( X - 1/2 ) . 5/2 = 7/4 - 1/2

( X - 1/2 ) . 5/2 = 5/4

 X - 1/2 = 5/4 : 5/2

X - 1/2 = 1/2

X = 1/2 + 1/2

X = 1/4

\(\left(x-\frac{1}{2}\right).\frac{5}{2}+\frac{1}{2}=\frac{7}{4}\)

<=>\(\left(x-\frac{1}{2}\right).\frac{5}{2}=\frac{5}{4}\)

<=>\(x-\frac{1}{2}=\frac{5}{4}:\frac{5}{2}\)

<=>\(x-\frac{1}{2}=\frac{1}{2}\)

<=>x=1

\(\frac{-22}{15}x+\frac{1}{3}=\left|\frac{-2}{3}+\frac{1}{5}\right|\)

=>\(\frac{-22}{15}x+\frac{1}{3}=\left|\frac{-7}{15}\right|\)

=>\(\frac{-22}{15}x+\frac{1}{3}=\frac{7}{15}\)

=>\(\frac{-22}{15}x=\frac{7}{15}-\frac{1}{3}\)

=>\(\frac{-22}{15}x=\frac{2}{15}\)

=>\(x=\frac{2}{15}:\frac{-22}{15}\)

=>\(x=\frac{1}{-11}\)

có 2 trường hợp:

*\(\frac{-22}{15}\)x +\(\frac{1}{3}\)=\(\frac{-7}{15}\)  HOẶC     \(\frac{-22}{15}\)x +\(\frac{1}{3}\)=\(\frac{7}{15}\)

Trường hợp 1: x=\(\frac{6}{11}\)                     Trường hợp 2: x=\(\frac{-1}{11}\)

Có 34 chữ số 0 ở tận cùng

\(\Leftrightarrow2^{x+1}.3^y=4^x.3^x\)

\(\Leftrightarrow2^{x+1}.3^y=2^{2x}.3^x\)

\(\Leftrightarrow\frac{3^y}{3^x}=\frac{2^{2x}}{2^{x+1}}\)

\(\Leftrightarrow3^{y-x}=2^{x-1}\)

Nếu \(x>1\Rightarrow\) vế trái lẻ, vế phải chẵn pt vô nghiệm

\(\Rightarrow x=1\Rightarrow3^{y-1}=1\Rightarrow y=1\)

Bài 1

a) \(P=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(=1-\frac{1}{10}\)

\(=\frac{10}{10}-\frac{1}{10}=\frac{9}{10}\)

b) \(S=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\)

\(=\frac{1}{3}-\frac{1}{99}\)

\(=\frac{33}{99}-\frac{1}{99}\)

\(=\frac{32}{99}\)

c)\(Q=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{19.20}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}\)

\(=\frac{10}{20}-\frac{1}{20}\)

\(=\frac{9}{20}\)

Tk mình nha!!

Câu 2:

\(P=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{99}\right)\)

\(=\left(\frac{2}{2}+\frac{1}{2}\right).\left(\frac{3}{3}+\frac{1}{3}\right).\left(\frac{4}{4}+\frac{1}{4}\right)...\left(\frac{99}{99}+\frac{1}{99}\right)\)

\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{100}{99}\)

\(=\frac{3\cdot4\cdot5...100}{2.3.4...99}\)

\(=\frac{3\cdot100}{2}\)

\(=\frac{300}{2}=150\)

3025 = (-55)² hoặc 3025 = 55² => x = 55 ; -55

\(x=\sqrt{3025}\)

\(x=55\)

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a. Ta có : \(x-8.2018⋮4\) mà \(8.2018⋮4\Rightarrow x⋮4\Rightarrow x\inƯ\left(4\right)=\left\{1;2;4\right\}\)

b.Ta có : \(75.2015-x⋮5\)mà \(75.2015⋮5\Rightarrow x⋮5\Rightarrow x\inƯ\left(5\right)=\left\{1;5\right\}\)