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Ta có:
a2017 + b2017 = a2017 + ab2016 + a2016b + b2017 - a2016b - ab2016
= a.(a2016 + b2016) + b.(b2016 + a2016) - ab.(a2015 - b2015)
= (a2016 + b2016).(a + b) - ab.(a2015 + b2015)
Chia cả 2 vế cho a2017 + b2017 = a2016 + b2016 = a2015 + b2015
=> a + b - ab = 1
=> a.(1 - b) - 1 + b = 0
=> a.(1 - b) - (1 - b) = 0
=> (1 - b).(a - 1) = 0
=> a = b = 1
Ta có: P = 20.a + 11.b + 2017
P = 20.1 + 11.b + 2017
P = 20 + 11 + 2017
P = 2048
theo bài ra ta có \(a^{2012}+b^{2012}=a^{2013}+b^{2013}=a^{2014}+b^{2014}\Rightarrow a^{2012}+b^{2012}-2\left(a^{2013}+b^{2013}\right)+a^{2014}+b^{2014}=0\)\(\Rightarrow a^{2012}+b^{2012}-2\left(a^{2013}+b^{2013}\right)+a^{2014}+b^{2014}=0\Leftrightarrow\)
\($\left(a^{1006}-a^{1007}\right)^2+\left(b^{1006}-b^{1007}\right)=0$\)
\(\Leftrightarrow\left\{\begin{matrix}a^{1006}-a^{1007}=0\\b^{1006}-b^{1007}=0\end{matrix}\right.\left\{\begin{matrix}a=0;a=1\\b=0;b=1\end{matrix}\right.\)
Khi đó P=20.0+11.0+2013=2013
hoặc P=20.1+11.0+2013=2033
hoặc p=20.0+11.1+2013=2024
\(\dfrac{a_1}{a_2}=\dfrac{a_2}{a_3}=...=\dfrac{a_{2013}}{a_{2014}}=\dfrac{a_{2014}}{a_1}=\dfrac{a_1+a_2+...+a_{2014}}{a_1+a_2+...+a_{2014}}=1\\ \Leftrightarrow a_1=a_2=...=a_{2014}\\ \Leftrightarrow Q=\dfrac{\left(2014a_1\right)^2}{a_1^2\left(1+2+...+2014\right)}=\dfrac{2014^2\cdot a_1^2}{a_1^2\cdot\dfrac{2015\cdot2014}{2}}=\dfrac{2\cdot2014^2}{2015\cdot2014}=\dfrac{2\cdot2014}{2015}=...\)
ta có \(a^{2012}+b^{2012}=a^{2013}+b^{2013}\)
\(\Rightarrow a^{2012}-a^{2013}+b^{2012}_{ }-b^{2013}=0\)
\(\Rightarrow a^{2012}\left(1-a\right)+b^{2012}\left(1-b\right)=0\)\(\left(1\right)\)
tương tự \(a^{2013}+b^{2013}=a^{2014}+b^{2014}\)
\(\Leftrightarrow a^{2013}\left(1-a\right)+b^{2013}\left(1-b\right)=0\)\(\left(2\right)\)
trừ (1) cho (2)
ta có \(\left(a^{2012}-a^{2013}\right)\left(1-a\right)\)\(+\left(b^{2012}-b^{2013}\right)\left(1-b\right)=0\)
\(\Leftrightarrow a^{2012}\left(1-a\right)^2+b^{2012}\left(1-b\right)^2=0\)
mà\(a^{2012}\left(1-a\right)^2\ge0;b^{2012}\left(1-b\right)^2\ge0\)
\(\Rightarrow a=1;b=1\)
\(\Rightarrow M=20\times1+11\times1+2013=2044\)
lay cai dau tru cai thu 2
xong lay cai thu 2 tru cai thu 3
xong lay ket qua dau tim dc tru ket qua sau la tim dc a=b=1
roi thay vao tinh M la xong