Question

已知x/y=1/2,求x^2+2xy+y^2/x^2-xy+y^2

Answer 1

你好

解
（x^2+2xy+y^2）/（x^2-xy+y^2）
=（x+y）^2/（x-y）^2 上下同除以y^2 得
=（x/y+1）^2/（x/y-1）^2
=（3/2）^2/（-1/2）^2
=（9/4）/（1/4）
=9

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Answer 2

x/y=1/2

y=2x
x^2+2xy+y^2/x^2-xy+y^2

=（x²+4x²+4x²）/（x²-2x²+4x²）
=9/3
=3

Answer 3

(x^2+2xy+y^2)/(x^2-xy+y^2) 分子分母同时除以y^2

=(x^2/y^2+2xy/y^2+y^2/y^2)/(x^2/y^2-xy/y^2+y^2/y^2)
=(x^2/y^2+2x/y+1)/(x^2/y^2-x/y+1)

=[(1/2)^2+2*1/2+1]/[(1/2)^2-1/2+1]
=(1/4+1+1)/(1/4-1/2+1)

=(9/4)/(3/4)

=3

Answer 4

分子分母同除以y^2,再代值