*2010/1+2009/2+...+1/2010

=(2009/2+1)+(2008/3+1)+...+(1/2010+1)+1

=2011/2+2011/3+..+2011/2010+2011/2011

=2011(1/2+1/3+1/4+...+1/2011)

=> C=2011/1=2011

=> (a+b+c)(1/a+b +a/b+c +1/c+a)=2010 . 1/2010 

=>(a+b+c) /(a+b) +(a+b+c)/(b+c) + (a+b+c)/(a+c)=1

=> 1 +c/a+b  + 1 +a/b+c + 1 +b/a+c=1

=>a/b+c +b/a+c +c/a+b =-2

Bài 1 : làm tương tự với bài 2;3 nhé

Ta có : \(f\left(0\right)=c=2010;f\left(1\right)=a+b+c=2011\)

\(\Rightarrow f\left(1\right)=a+b=1\)

\(f\left(-1\right)=a-b+c=2012\Rightarrow f\left(-1\right)=a-b=2\)

\(\Rightarrow a+b=1;a-b=2\Rightarrow2a=3\Leftrightarrow a=\dfrac{3}{2};b=\dfrac{3}{2}-2=-\dfrac{1}{2}\)

Vậy \(f\left(-2\right)=4a-2b+c=\dfrac{4.3}{2}-2\left(-\dfrac{1}{2}\right)+2010=6+1+2010=2017\)

Ta có: \(M=\frac{2010a}{ab+2010a+2010}+\frac{b}{bc+b+2010}+\frac{c}{ac+c+1}\)

Thế: abc = 2010 ta được:

\(M=\frac{a^2bc}{ab+a^2bc+abc}+\frac{b}{bc+b+abc}+\frac{c}{ac+c+1}\)

\(\Leftrightarrow\frac{a^2bc}{ab\left(1+ac+c\right)}+\frac{b}{b\left(c+1+ac\right)}+\frac{c}{ac+c+1}\)

\(\Leftrightarrow\frac{a^2bc}{ab\left(1+ac+c\right)}+\frac{ab}{ab\left(c+1+ac\right)}+\frac{abc}{ab\left(ac+c+1\right)}\)

\(\Leftrightarrow\frac{a^2bc+ab+abc}{ab\left(1+ac+c\right)}=\frac{ab\left(ac+1+c\right)}{ab\left(1+ac+c\right)}=1\)

Vậy \(M=1\)

Ta có:\(1-\frac{2010}{2010}=1-1=0\)

Tích A= (1-1/2010).(1-2/2010).(1-3/2010)....(1-2011/2010) chứa thừa số \(1-\frac{2010}{2010}=0\)

Vậy tích A=(1-1/2010).(1-2/2010).(1-3/2010)....(1-2011/2010)=0(Vì có chứa thừa số 0)

Ta có \(1-\frac{2010}{2010}=1-1=0\)

Mà \(A=\left(1-\frac{1}{2010}\right).\left(1-\frac{2}{2010}\right).\left(1-\frac{3}{2010}\right)...\left(1-\frac{2010}{2010}\right).\left(1-\frac{2011}{2010}\right)\)

Nên \(A=...0\)\(=0\)

Bạn giải cũng được đấy alibaba nguyễn, nhưng theo mình thì làm cách này dễ hiểu hơn!

Ta có: \(C=\frac{\frac{2010}{1}+\frac{2009}{2}+\frac{2008}{3}+...+\frac{1}{2010}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}}\)

Đặt \(A=\frac{2010}{1}+\frac{2009}{2}+\frac{2008}{3}+...+\frac{1}{2010}\)

\(A=\frac{2010}{1}+1+\frac{2009}{1}+1+\frac{2008}{1}+1+...+\frac{1}{2010}+1-2010\)

\(=\frac{2011}{1}+\frac{2011}{2}+\frac{2011}{3}+...+\frac{2011}{2010}-\frac{2011.2010}{2011}\)

\(=2011\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}-\frac{2010}{2011}\right)\)

Đặt \(B=\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}\)

\(B=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}-1\)

\(=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}-\frac{2010}{2011}\)

Ta có: \(C=\frac{A}{B}=2011\)(lấy A-B)

Ta có :

\(2010A=\dfrac{2010^{2012}+2010}{2010^{2012}+1}=\dfrac{2010^{2012}+1+2009}{2010^{2012}+1}=1+\dfrac{2009}{2010^{2012}+1}\)

\(2010B=\dfrac{2010^{2011}+2010}{2010^{2011}+1}=\dfrac{2010^{2011}+1+2009}{2010^{2011}+1}=1+\dfrac{2009}{2010^{2011}+1}\)

Vì \(1+\dfrac{2009}{2010^{2012}+1}< 1+\dfrac{2009}{2010^{2011}+1}\Rightarrow A< B\)

~ Học tốt ~

Thiên bình có 102 :

spam vừa thôi mk có hỏi bài đấy đâu!

Ta có : a²⁰¹⁰ + b²⁰¹⁰ + c²⁰¹⁰ = a¹⁰⁰⁵b¹⁰⁰⁵ + b¹⁰⁰⁵c¹⁰⁰⁵ + c¹⁰⁰⁵a¹⁰⁰⁵ 

<=> 2a²⁰¹⁰ + 2b²⁰¹⁰ + 2c²⁰¹⁰ = 2a¹⁰⁰⁵b¹⁰⁰⁵ + 2b¹⁰⁰⁵c¹⁰⁰⁵ + 2c¹⁰⁰⁵a¹⁰⁰⁵ 

<=> 2a²⁰¹⁰ + 2b²⁰¹⁰ + 2c²⁰¹⁰  - 2a¹⁰⁰⁵b¹⁰⁰⁵ - 2b¹⁰⁰⁵c¹⁰⁰⁵ - 2c¹⁰⁰⁵a¹⁰⁰⁵ = 0

<=> (a²⁰¹⁰ - 2a¹⁰⁰⁵b¹⁰⁰⁵ + b²⁰¹⁰) + (b²⁰¹⁰ - 2b¹⁰⁰⁵c¹⁰⁰⁵ + c²⁰¹⁰) + (c²⁰¹⁰ - 2c¹⁰⁰⁵a¹⁰⁰⁵  +  a²⁰¹⁰​) = 0

<=> (a¹⁰⁰⁵ - b¹⁰⁰⁵)² + (b¹⁰⁰⁵ - c¹⁰⁰⁵)² + (c¹⁰⁰⁵ - a¹⁰⁰⁵ ​)² = 0

=> a¹⁰⁰⁵ - b¹⁰⁰⁵ = b¹⁰⁰⁵ - c¹⁰⁰⁵ = c¹⁰⁰⁵ - a¹⁰⁰⁵ ​ = 0

=> a = b = c 

Vậy (a - b)²⁰ + (b - c)¹¹ + (c - a)²⁰¹⁰ = (a - a)²⁰ + (a - a)¹¹ + (a - a)²⁰¹⁰ = 0 + 0 + 0 = 0 .

       a²⁰¹⁰ + b²⁰¹⁰ + c²⁰¹⁰ = a¹⁰⁰⁵b¹⁰⁰⁵ + b¹⁰⁰⁵c¹⁰⁰⁵ + c¹⁰⁰⁵a¹⁰⁰⁵ 

<=> 2a²⁰¹⁰ + 2b²⁰¹⁰ + 2c²⁰¹⁰ = 2a¹⁰⁰⁵b¹⁰⁰⁵ + 2b¹⁰⁰⁵c¹⁰⁰⁵ + 2c¹⁰⁰⁵a¹⁰⁰⁵ 

<=> 2a²⁰¹⁰ + 2b²⁰¹⁰ + 2c²⁰¹⁰  - 2a¹⁰⁰⁵b¹⁰⁰⁵ - 2b¹⁰⁰⁵c¹⁰⁰⁵ - 2c¹⁰⁰⁵a¹⁰⁰⁵ = 0

<=> (a²⁰¹⁰ - 2a¹⁰⁰⁵b¹⁰⁰⁵ + b²⁰¹⁰) + (b²⁰¹⁰ - 2b¹⁰⁰⁵c¹⁰⁰⁵ + c²⁰¹⁰) + (c²⁰¹⁰ - 2c¹⁰⁰⁵a¹⁰⁰⁵  +  a²⁰¹⁰​) = 0

<=> (a¹⁰⁰⁵ - b¹⁰⁰⁵)² + (b¹⁰⁰⁵ - c¹⁰⁰⁵)² + (c¹⁰⁰⁵ - a¹⁰⁰⁵ ​)² = 0

=> a¹⁰⁰⁵ - b¹⁰⁰⁵ = b¹⁰⁰⁵ - c¹⁰⁰⁵ = c¹⁰⁰⁵ - a¹⁰⁰⁵ ​ = 0

=> a = b = c