若x-y=2,xy=48,则X的4次+y的4次=

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若x-y=2,xy=48,则X的4次+y的4次=若x-y=2,xy=48,则X的4次+y的4次=若x-y=2,xy=48,则X的4次+y的4次=x-y=2两边平方x^2-2xy+y^2=4x^2+y^

若x-y=2,xy=48,则X的4次+y的4次=
若x-y=2,xy=48,则X的4次+y的4次=

若x-y=2,xy=48,则X的4次+y的4次=
x-y=2
两边平方
x^2-2xy+y^2=4
x^2+y^2=4+2xy=4+96=100
两边平方
x^4+2x^2y^2+y^4=10000
x^4+y^4=10000-2(xy)^2=10000-2*2304=5392

x-y=2
(x-y)^2 = 2^2
x^2 - 2xy + y^2 = 4
xy = 48,=======>x^2 + y^2 = 100
(x^2 + y^2)^2 = 100^2
x^4 + y^4 + 2(xy)^2 = 10000
x^4 + y^4 = 10000 - 2(xy)^2 = 10000 - 2 * 48^2 = 5 392

x^4+y^4=(x^2+y^2)^2-2(xy)^2=[(x-y)^2+2xy]^2-2(xy)^2
=(2^2+2*48)^2-2*(48^2)
=5392

x-y=2
x^2-2xy+y^2=4
x^2+y^2=4+2xy=100
x^4+y^4=10000-2x^2y^2=10000-4608=5392