已知x的2次方+y的2次方=8又4分之1,x-y=7.5,求{xy}的4次方的值

2025-05-05 13:10:04
推荐回答(2个)
回答1:

x²+y² = 8+1/4 = 33/4 ......(1)
x-y=7.5 = 15/2
(x-y)² = x²+y²-2xy = (15/2)² = 225/4 ......(2)
(1)-(2):2xy = 33/4-225/4 = -192/4= -48
xy= -24
(xy)^4 = (-24)^4 = 331776

回答2:

x^2+y^2=33/4,
x-y=15/2,所以(x-y)^2=x^2+y^2-2xy=225/4,得xy=-24,所以(xy)^4=331776。