Question

数学天才请进已知x/y=2/7,求x 2-3xy+2y 2/2x 2-3xy+7y 2的值若x/3=y/2=z/5,求分

Answer 1

令x=2k y=7k代入

x 2-3xy+2y 2/2x 2-3xy+7y 2=4k^2-42k^2+98k^2/(8k^2-42k^2+343k^2)=20/103

同理令x=3k y=2k z=5k 代入xy+yz+zx/x 2+y 2+Z 2

=6+10+15/（9+4+25）=31/38

x 2-3x+1=0

x-3+1/x=0

x+1/x=3

(x+1/x)^2=9

x^2+1/x^2+2=9

x^2+1/x^2=7

^2为平方