Question

已知X+Y=6且XY=4,则（X+Y)的平方=（ ）；X的四次方+Y的四次方=（ ）

Answer 1

(x+y)^2=6^2=36

x^2+y^2+2xy=(x+y)^2=36

则x^2+y^2=36-2xy=36-8=28

x^4+y^4=x^4+y^4+2x^2y^2-2x^2y^2=(x^2+y^2)^2-2(xy)^2=28^2-2*4^2=752