Giải.

Ta có : \(P=2013^0+2013^1+....+2013^{2017}\)

\(\Rightarrow2013P=2013^1+2013^2+...+2013^{2018}\)

\(2012P=2013P-P=2013^{2018}-2013^0\)

\(\Leftrightarrow2012P=2013^{2018}-1\)

Vậy \(2012P+1=2013^{2018}-1+1=2013^{2018}\)

tik mik nha !!!

Giải.

a) \(\left|3x+1\right|+\left|2y-1\right|=0\)

Nhận xét : Do \(\left|3x+1\right|\ge0\) với \(\forall x\)

và \(\left|2y-1\right|\ge0\) với \(\forall y\)

Nên \(\left|3x+1\right|+\left|2y-1\right|=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left|3x+1\right|=0\\\left|2y-1\right|=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+1=0\\2y-1=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-1}{3}\\y=\dfrac{1}{2}\end{matrix}\right.\)

Vậy \(x=\dfrac{-1}{3}\) và \(y=\dfrac{1}{2}\)

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Ta có:

\(C=\dfrac{1}{4}+\dfrac{2}{4^2}+\dfrac{3}{4^3}+...+\dfrac{2017}{4^{2017}}\)

\(4C=1+\dfrac{2}{4}+\dfrac{3}{4^2}+\dfrac{4}{4^3}+...+\dfrac{2017}{4^{2016}}\)

\(\Rightarrow3C=4C-C=1+\dfrac{1}{4}+\dfrac{1}{4^2}+...+\dfrac{1}{4^{2016}}-\dfrac{2017}{4^{2017}}\)Đặt \(D=1+\dfrac{1}{4}+\dfrac{1}{4^2}+...+\dfrac{1}{4^{2016}}\)

\(\Rightarrow4D=4+1+\dfrac{1}{4}+...+\dfrac{1}{4^{2015}}\)

\(\Rightarrow3D=4D-D=4-\dfrac{1}{4^{2016}}\)

Ta có : Do \(4-\dfrac{1}{4^{2016}}< 4\Rightarrow3D< 4\)

\(\Rightarrow D< \dfrac{4}{3}\)

Thay giá trị tìm được của D vào 3C được:

\(3C=4-\dfrac{1}{4^{2016}}-\dfrac{2017}{4^{2017}}\)

Do \(D< \dfrac{4}{3}\Rightarrow D-\dfrac{2017}{4^{2017}}< \dfrac{4}{3}\)

Hay \(3C< \dfrac{4}{3}\Rightarrow C< \dfrac{4}{9}< \dfrac{1}{2}\Rightarrow C< \dfrac{1}{2}\left(đpcm\right)\)

Vậy....

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\(\left(x-\dfrac{1}{3}\right)^2-\dfrac{1}{4}=0\)

\(\Leftrightarrow\left(x-\dfrac{1}{3}\right)^2=\dfrac{1}{4}\)

\(\Leftrightarrow\left(x-\dfrac{1}{3}\right)^2=\left(\pm\dfrac{1}{2}\right)^2\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{3}=\dfrac{1}{2}\\x-\dfrac{1}{3}=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{6}\\x=\dfrac{-1}{6}\end{matrix}\right.\)

Vậy...

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1.

a) \(3^{x+2}+3^x=90\)

\(\Leftrightarrow3^x\left(3^2+1\right)=90\)

\(\Leftrightarrow3^x.10=90\)

\(\Leftrightarrow3^x=9=3^2\)

\(\Leftrightarrow x=2\)

vậy...

b) \(\left(x+\dfrac{1}{2}\right)^2-\dfrac{1}{3}=\dfrac{1}{9}\)

\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2=\dfrac{4}{9}\)

\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2=\left(\pm\dfrac{2}{3}\right)^2\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{2}{3}\\x+\dfrac{1}{2}=-\dfrac{2}{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{6}\\x=\dfrac{-7}{6}\end{matrix}\right.\)

Vậy...

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Giải.

Ta có : \(\dfrac{x}{5}=\dfrac{45}{x}\Leftrightarrow x.x=45.5\)

\(\Leftrightarrow x^2=225=\left(\pm15\right)^2\)

\(\left[{}\begin{matrix}x=15\\x=-15\end{matrix}\right.\)

Vậy \(x=15\) hoặc \(x=-15\)

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1.

a) \(\left(2x-\dfrac{1}{6}\right)^2+\left|3y+12\right|\le0\)

Nhận xét : Do \(\left(2x-\dfrac{1}{6}\right)^2\ge0\) với \(\forall x\)

Và \(\left|3y+12\right|\ge0\) với \(\forall y\)

Nên \(\left(2x-\dfrac{1}{6}\right)^2+\left|3y+12\right|\le0\)

\(\Leftrightarrow\left(2x-\dfrac{1}{6}\right)^2+\left|3y+12\right|=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(2x-\dfrac{1}{6}\right)^2=0\\\left|3y+12\right|=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x-\dfrac{1}{6}=0\\3y+12=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{12}\\y=-4\end{matrix}\right.\)

vậy \(x=\dfrac{1}{12};y=-4\)

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1.Quynh and Nga work in the city center

->Where do Quynh and Nga work ?

2.There is a swimming pool near Tuong's house

->What is there near Tuong's house ?

3.Our family are going on holiday by car

->How are your family going on holiday ?

4.Mrs.Huong and her husband are going to stay in Ha Long for one week

->How long are Mrs Huong and her husband going to stay in Ha Long ?

5.Our new classmates usually get up at five in the morning because they live far from our school

->Why does your classmates usually get up at 5 in the morning ?

tik mik nha !!!!

a) 1,5 + 2,5 + 3,5 + 4,5 + 5,5 + 6,5 + 7,5 + 8,5 = (1,5 + 8,5) + (2,5 + 7,5) + ... + (4,5 + 6,5) + 5,5 

                                                                    = 10 + 10 + 10 + 10 + 5,5

                                                                    = 45,5

Giai đoạn lợn choai có khối lượng?

A. 5 – 10 kg

B. 20 – 30 kg

C. 20 – 50kg

D. 30 – 60kg