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已知x/y+z=a,y/x+z=b,z/x+y=c求a/a+1+b/b+1+c/c+1
题目详情
已知x/y+z=a,y/x+z=b,z/x+y=c求a/a+1+b/b+1+c/c+1
▼优质解答
答案和解析
x/（y+z）=a, 1/a=(y+z)/x 1/a+1=(x+y+x)/x a/(a+1)=x/(x+y+z)
y/（z+x）=b, 化为b/(b+1)=y/(x+y+z)
z/（x+y）=c 化为c/(c+1)=z/(x+y+z)
三式相加：a/(a+1)+b/(b+1)+c/(c+1)=(x+y+z)/(x+y+z)=1
y/（z+x）=b, 化为b/(b+1)=y/(x+y+z)
z/（x+y）=c 化为c/(c+1)=z/(x+y+z)
三式相加：a/(a+1)+b/(b+1)+c/(c+1)=(x+y+z)/(x+y+z)=1
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