Question

cho x+y=-3 và x.y=-28.tính giá trị các biểu thức theo m,n

a, x^2+y^2

b,x^3+y^3

c,x^4+y^4

Answer 1

\(a,x^2+y^2=\left(x+y\right)^2-2xy=\left(-3\right)^2-2.\left(-28\right)=65\)

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

\(=\left(x+y\right)^3-3xy\left(x+y\right)\)

\(=\left(-3\right)^3-3.\left(-28\right).\left(-3\right)=-279\)

\(c,x^4+y^4=\left(x+y\right)^4-4x^3y-4xy^3-6x^2y^2\)

\(=\left(x+y\right)^4-4xy\left(x^2+y^2\right)-6\left(xy\right)^2\)

\(=\left(-3\right)^4-4.\left(-28\right).65-6.\left(-28\right)^2=2657\)