Question

X1+x2=7
x1*x2=2
X1^4 + x2^4=?
(^4 степень)

Answer 1

$x_1^4+x_2^4=(x_1^2)^2+(x_2^2)^2=(x_1^2)^2+2x_1^2x_2^2+(x_2^2)^2-2x_1^2x_2^2=\\ \\ =(x_1^2+x_2^2)^2-2(x_1x_2)^2=(x_1^2+2x_1x_2+x_2^2-2x_1x_2)^2-2(x_1x_2)^2=\\ \\ =((x_1+x_2)^2-2x_1x_2)^2-2(x_1x_2)^2=(7^2-2\cdot2)^2-2\cdot2^2=\\ \\ =(49-4)^2-2\cdot4=45^2-8=2025-8=2017$