x+y=1 xy=-1 求x立方+y立方?求x的4次方+y的4次方?好的话有更高的酬劳哦!
问题描述：
x+y=1 xy=-1 求x立方+y立方?求x的4次方+y的4次方?
好的话有更高的酬劳哦!
答
∵x+y=1 xy=-1
∴x³+y³=（x+y）（x²-xy+y²）=（x+y）[(x+y）²-3xy]=1×（1+3）=4
x的4次方+y的4次方
=（x²）²+（y²）²
=（x²+y²）²-2x²y²
=[(x+y)²-2xy]²-2（xy）²
=[1+2]²-2
=9-2=7
答
x的4次方＋y的4次方=(x²＋y²)²－2(xy)²=(x²＋y²)²－2
而x²＋y²=(x＋y)²－2xy=1＋2=3
则：x的4次方＋y的4次方=3²－2=7
答
x³+y³
=(x+y)(x²-xy+y²)
=(x+y)[(x+y)²-3xy]
=1×[1²-3×(-1)]
=1×(1+3)
=1×4
=4
x^4+y^4
=(x^4+y^4+2x²y²)－2x²y²
=(x²+y²)²－2x²y²
=[(x+y)²－2xy]²－2x²y²
=[1²－2×(-1)]²－2×(-1)²
=(1+2)²-2×1
=3²-2
=9-2
=7