dat x+1/x=k.Ta co: x²+1/x²=k²-2,thay vao phuong trinh ta duoc:k²-2-4k+6=0\(\Leftrightarrow\)k²-4k+4=0\(\Leftrightarrow\)(k-2)²=0\(\Leftrightarrow\)k-2=0\(\Leftrightarrow\)k=2.Suy ra:x+1/x=2\(\Leftrightarrow\)x²+1=2x\(\Leftrightarrow\)x²-2x+1=0\(\Leftrightarrow\)(x-1)²=0\(\Leftrightarrow\)x-1=0\(\Leftrightarrow\)x=1.Vay phuong trinh tren co nghiem la x=1

tu 1 den 1000 co: (1000 - 1):1+1 =1000(so)

tu 1 den 1000 co : 1000:2 = 500 (cap)

vay 1+2+3+4+5+6+........+997+998+999+1000

= (1000+1) . 500

=500500

 k cho mik nha ^_^ ^_^ ^_^

1<2 là đúng => 1>2 là sai

\(a.\dfrac{15}{x-9}=\dfrac{20}{y-12}=\dfrac{40}{z-24}\&xy=1200\)

\(\Leftrightarrow\dfrac{15}{20}=\dfrac{x-9}{y-12}\Leftrightarrow\dfrac{3}{4}=\dfrac{x-9}{y-12}\)

\(\Rightarrow\dfrac{9}{12}=\dfrac{x-9}{y-12}\)

Áp dụng tính chất dãy tỉ số bằng nhau:

\(\dfrac{9}{12}=\dfrac{x-9}{y-12}=\dfrac{x-9+9}{y-12+12}=\dfrac{x}{y}\)

\(\Rightarrow\dfrac{x}{y}=\dfrac{xy}{y^2}=\dfrac{x^2}{xy}\)

Từ \(\dfrac{3}{4}=\dfrac{xy}{y^{^2}}\Rightarrow\dfrac{3}{4}=\dfrac{1200}{y^2}\Rightarrow y^2=1200.\dfrac{4}{3}=1600\)

\(\Rightarrow y=\sqrt{1600}=\pm40\)

+ TH1: \(y=40\Rightarrow x=30\)

\(\dfrac{15}{x-9}=\dfrac{40}{z-24}\Rightarrow z=80\) (tự giải pt)

+ TH2: \(y=-40\Rightarrow x=-30\)

\(\dfrac{15}{x-9}=\dfrac{40}{z-4}\Rightarrow z=-80\) (tự giải pt)

Vậy, các cặp \(\left(x;y;z\right)\) thỏa mãn là \(\left(30;40;80\right)\&\left(-30;-40;-80\right)\)

\(a.A=2015^2=2015\left(2014+1\right)=2015.2014+2015\)

\(B=2014.2016=2014.\left(2015+1\right)=2015.2014+2014\)

Vì \(2015>2014\Rightarrow2015.2014+2015>2015.2014+2014\)

\(\Rightarrow A>B\)

\(b.C=3^{16}-1\)

\(D=8.\left(3^2+1\right).\left(3^4+1\right).\left(3^8+1\right)\)

\(=\left(3^2-1\right)\left(3^2+1\right).\left(3^4+1\right).\left(3^8+1\right)\)

\(=\left(3^4-1\right).\left(3^4+1\right).\left(3^8+1\right)=\left(3^8-1\right)\left(3^8+1\right)=3^{16}-1\)

Vì \(3^{16}-1=3^{16}-1\Rightarrow C=D\)

Dấu hiệu chia hết cho 2 là các số chẵn.

Dấu hiệu chia hết cho 5 là các số có đuôi là 0 và 5

100+198=298

dễ quá

Đặt A=1+2+2²+............+2²⁰¹²

2A=2+2²+2³+..............+2²⁰¹³

2A-A=2²⁰¹³-1

A=2²⁰¹³-1

=>M=\(\frac{2^{2013}-1}{2^{2014}-2}=\frac{2^{2013}-1}{2^{2013}.2-2}=\frac{2^{2013}-1}{2.\left(2^{2013}-1\right)}=\frac{1}{2}\)