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若x/2=y/3,求x^2-xy-y^2/x^2-xy-y^2的值急
题目详情
若x/2=y/3,求x^2-xy-y^2/x^2-xy-y^2的值 急
▼优质解答
答案和解析
(x^2-xy-y^2)/(x^2-xy-y^2)=1 /
x/2=y/3
x/y=2/3
(x^2-xy-y^2)/(x^2-xy-y^2)分子分母同时除以y^2
=(x^2/y^2-xy/y^2-y^2/y^2)/(x^2/y^2-xy/y^2-y^2/y^2)
=(x^2/y^2-x/y-1)/(x^2/y^2-x/y-1)
=[(2/3)^2-2/3-1]/[(2/3)^2-2/3-1]
=[4/9-5/3]/[4/9-5/3]
=1
x/2=y/3
x/y=2/3
(x^2-xy-y^2)/(x^2-xy-y^2)分子分母同时除以y^2
=(x^2/y^2-xy/y^2-y^2/y^2)/(x^2/y^2-xy/y^2-y^2/y^2)
=(x^2/y^2-x/y-1)/(x^2/y^2-x/y-1)
=[(2/3)^2-2/3-1]/[(2/3)^2-2/3-1]
=[4/9-5/3]/[4/9-5/3]
=1
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