Question

Cho x=\(\dfrac{\sqrt{2}-1}{2}\) và y=\(\dfrac{-\sqrt{2}-1}{2}\) . Tính B=\(x^7+y^7\)

Answer 1

cho cmt để tí nữa làm.

Answer 2

\(\left\{{}\begin{matrix}x+y=-1\\xy=-\dfrac{1}{4}\end{matrix}\right.\)

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

\(x^3+y^3=\left(x+y\right)^3-3xy\left(x+y\right)=1-3.\dfrac{1}{4}.1=\dfrac{1}{4}\)

\(x^4+y^4=\left(x^2+y^2\right)^2-2\left(xy\right)^2=\dfrac{9}{4}-2.\dfrac{1}{16}=\dfrac{17}{8}\)

\(x^7+y^7=\left(x^4+y^4\right)\left(x^3+y^3\right)-x^3y^3\left(x+y\right)=\dfrac{17}{8}.\dfrac{1}{4}-\dfrac{1}{4^3}.\left(-\dfrac{1}{4}\right)=\dfrac{1}{4}.\dfrac{35}{64}=\dfrac{35}{256}.\)

Answer 3

Sách phát triển toán 9 hoặc trên google có rất nhiều!