已知x^2+y^2=5 xy=2 计算:(1) (x+y)^2 (2) x-y (3) x^4+y^4如题
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![已知x^2+y^2=5 xy=2 计算:(1) (x+y)^2 (2) x-y (3) x^4+y^4如题](/uploads/image/z/1101696-24-6.jpg?t=%E5%B7%B2%E7%9F%A5x%5E2%2By%5E2%3D5+xy%3D2+%E8%AE%A1%E7%AE%97%3A%281%29+%28x%2By%29%5E2+%282%29+x-y+%283%29+x%5E4%2By%5E4%E5%A6%82%E9%A2%98)
已知x^2+y^2=5 xy=2 计算:(1) (x+y)^2 (2) x-y (3) x^4+y^4如题
已知x^2+y^2=5 xy=2 计算:(1) (x+y)^2 (2) x-y (3) x^4+y^4
如题
已知x^2+y^2=5 xy=2 计算:(1) (x+y)^2 (2) x-y (3) x^4+y^4如题
x^2+y^2=5,xy=2
(x+y)^2=x^2+y^2+2xy=5+2*2=9
(x-y)^2=x^2+y^2-2xy=5-2*2=1
∴(1)(x+y)^2=9
(2)x-y=±1
(3)x^4+y^4=(x^2+y^2)^2-2x^2y^2
=(x^2+y^2)^2-2*(xy)^2
=5^2-2*2^2
=25-8
=17
(x+y)^2=x^2+y^2+2xy=9
(x-y)^2=x^2+y^2-2xy=1 x-y=±1
x^4+y^4=(x^2+y^2)^2-2x^2y^2=25-2*4=17