Question

初二上学期数学题求解

已知x+y=4，xy=1/2，求x四次方+y四次方的值
要详细步骤

Answer 1

x^4+y^4=x^4+2x²y²+y^4-2x²y²=(x²+y²)²-2x²y²
x²+y²=(x+y)²-2xy=16-1=15
2x²y²=1/2
所以225-1/2=449/2

Answer 2

因为X+Y=4
XY=1/2
所以X^2+Y^2=(X+Y)^2-2XY=15
X^2*Y^2=1/4
所以X^4+Y^4=(X^2+Y^2)^2-2X^2*Y^2
=15^2-2*(1/4)
=224.5