Question

已知X²-y²=4Xy 求x的4次方+y的4次方/x²y²的值

Answer 1

由于X²-y²=4xy，两边同时除以xy，得到
(x/y)-(y/x)=4
令x/y=t，则y/x=1/t
于是得到
t-1/t=4，

(x^4+y^4)/x²y²
=(x/y)²+(y/x)²
=t²+1/t²
=(t-1/t)²+2
=4²+2
=18

Answer 2

x的4次方+y的4次方/x²y²
=[(x^4+y^4-2x^2y^2)+2x^2y^2]/x^2y^2
=[(x^2-y^2)^2+2x^2y^2]/x^2y^2
=[16x^2y^2+2x^2y^2]/x^2y^2
=18x^2y^2/x^2y^2
=18

Answer 3

X2－y2＝4xy 俩边同除xy得x／y－x／y＝4
∴(x／y－x／y)2＝16
∴(x／y)2＋(x／y)2＝16＋2＝18
∴(x4＋y4)／x2y2＝(x／y)2＋(x／y)2＝18

Answer 4

X²-y²=4Xy y/x-x/y=4 y^2/x^2+x^2/y^2=18

x的4次方+y的4次方/x²y²= y^2/x^2+x^2/y^2=18

Answer 5

(x^4+y^4)/x^2y^2=[(X²-y²)^2+2x^2y^2}/x^2y^2=[(4xy)^2+2x^2y^2]/x^2y^2=18