Question

Giúp mình vs

Answer 1

a) \(A_1=x^2+y^2=\left(x+y\right)^2-2xy=2^2-2.1=4-2=2\)

b) \(A_2=x^3+y^3=\left(x+y\right)^3-3xy\left(x+y\right)=2^3-3.1.2\)

\(=8-6=2\)

c) \(A_3=x^4+y^4=\left(x^2\right)^2+\left(y^2\right)^2=\left(x^2+y^2\right)^2-2x^2y^2\)

\(=\left(\left(x+y\right)^2-2xy\right)^2-2\left(xy\right)^2=\left(2^2-2.1\right)^2-2.1^2\)

\(=\left(4-2\right)^2-2=2^2-2=4-2=2\)