1.若a/b=c/d,求证(a²+c²)/(ab+cd)=(ab+cd)/(b²+d²)
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1.若a/b=c/d,求证(a²+c²)/(ab+cd)=(ab+cd)/(b²+d²)
1.若a/b=c/d,求证(a²+c²)/(ab+cd)=(ab+cd)/(b²+d²)
1.若a/b=c/d,求证(a²+c²)/(ab+cd)=(ab+cd)/(b²+d²)
(a²+c²)/(ab+cd)=(ab+cd)/(b²+d²),十字相乘得:
左边:(a²+c²)(b²+d²)=a²b²+c²b²+a²d²+c²d²
右边: (ab+cd)(ab+cd)=a²b²+c²d²+abcd+abcd,
由于a/b=c/d,得ad=bc,带入右边的: = a²b²+c²d²+aadd+cdcd=a²b²+c²b²+a²d²+c²d².
左 = 右 所以成立,的证 .
注意: 这种 只要证明 左==右即可 ,利用已知条件 ,你看看
若a/b=c/d 则 ad-bc=0
(a²+c²)/(ab+cd)=(ab+cd)/(b²+d²)等价于(ab+cd)*(ab+cd)=(a²+c²)(b²+d²)
展开 左边=a²b²+c²d²+2abcd
右边=a²b²+c²d²+c²b²+a²d²
左边-右边=(ad-bc)^2=0
得证