已知:x^2+y^2=17,xy=-4,且x>y,求x-y和x^2-y^2的值.
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已知:x^2+y^2=17,xy=-4,且x>y,求x-y和x^2-y^2的值.
已知:x^2+y^2=17,xy=-4,且x>y,求x-y和x^2-y^2的值.
已知:x^2+y^2=17,xy=-4,且x>y,求x-y和x^2-y^2的值.
x^2+y^2=17 xy=-4
故x^2+y^2-2xy=(x-y)^2=17-2(-4)=25,且x>y,故x-y=5
同理 x+y=3 故x^2-y^2=(x-y)(x+y)=3*5=15
x=4,y=-1 X-Y=5 x平方-Y平方=15
∵(x-y)²
=x²+y²-2xy
=17-2×(-4)
=17+8
=25
又x>y,则x-y>0
∴x-y=5
(x+y)²
=(x-y)²+4xy
=5²+4×(-4)
=25-16
=9
∴x+y=3
∴x²-y²
=(x+y)(x-y)
=3×5
=15
先给 xy=-4 这个等式两边平方,
那么得到x^2y^2=16,
结合x^2+y^2=17,且x>y,
可以得出x^2=16,y^2=1
因为xy=-4,又x>y,所以x=4,y=-1
则x-y=5,x^2-y^2=15