Question

已知实数a,b满足(a+b)^2=2b^2+ab且a,b同号,则a+b/a-b=

Answer 1

(a+b)^2=2b^2+ab所以a^2+2ab+b^2=2b^2+aba^2-ab=b^2a(a-b)=b^2b/(a-b)=a/b又a^2-ab=b^2所以a^2-ab-b^2=0把a看作未知数a=(b±√5b^2)/2=b(1±√5)/2a/b=(1±√5)/2ab同号,所以a/b>0a/b=(1+√5)/2(a+b)/(a-b)=(a-b+2b)...