Cho $a=\frac{-1+\sqrt{2}}{2};b=\frac{-1-\sqrt{2}}{2}$.Tính $a^7+b^7$.
cụ lớp 6 k bik làm mấy cái này đâu –  AKIRA 25-02-16 09:26 PM
cụ làm đi cho tôi đừng ngời đấy mà phán :) –  111aze 25-02-16 09:14 PM
a , b là nghiệm của pt đấy . tách thằng a^7 b^7 ra rùi thay vào –  AKIRA 25-02-16 09:01 PM
vcl ..... –  111aze 25-02-16 08:57 PM
Cái này tính ra xong mũ 7 lên ......@@~ –  Cường GVer 25-02-16 08:56 PM
cái này lấy thay a vào bậc 7 kên là ra =)))))))))))))) –  AKIRA 25-02-16 08:47 PM
đúng r bạn :) –  111aze 25-02-16 08:44 PM
cái này ở violympic phải ko pn? –  ๖ۣۜConan♥doyleღ 25-02-16 08:40 PM
=-239/64 –  ๖ۣۜConan♥doyleღ 25-02-16 08:39 PM
kết quả là phân số đúng ko? –  ๖ۣۜConan♥doyleღ 25-02-16 08:39 PM
dân 3k hỏi dân 1k =))) –  AKIRA 25-02-16 08:28 PM
Ta có $a+b=-1,ab=-\frac 14$
 Dễ thấy $ a^3+b^3=(a+b)^3-3ab(a+b)=-\frac 74$
$a^4+b^4=(a^2+b^2)^2-2a^2b^2=[(a+b)^2-2ab]^2-2a^2b^2=\frac {17}8$
$a^7+b^7=(a^4+b^4)(a^3+b^3)-a^3b^3(a+b)=\frac {-239}{64}$

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