Question

x+y=1 xy=-1 求x立方+y立方?求x的4次方+y的4次方?

Answer 1

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