Question

mọi người giúp e với ạ E cảm ơn

Answer 1

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

\(F=x^8+y^8\)

\(\Leftrightarrow F=\left(x^4+y^4\right)^2-2\left(xy\right)^4\)

\(\Leftrightarrow F=\left[\left(x^2+y^2\right)^2-2\left(xy\right)^2\right]^2-2\left(xy\right)^4\)

\(\Leftrightarrow F=\left\{\left[\left(\left(x+y\right)^2-2xy\right)^2-2\left(xy\right)\right]^2\right\}^2-2\left(xy\right)^4\)

\(\Leftrightarrow F=\left\{\left[\left(\left(1\right)^2-2.\left(-1\right)\right)^2-2\left(-1\right)^2\right]\right\}^2-2\left(-1\right)^4\)

\(\Leftrightarrow F=\left\{\left[9-2\right]\right\}^2-2=49-2=47\)