n满足方程log9(m)=log12(n)=log16(m+n),求n/m设Log9m=log12n=log16(m+n)=athen m=9^a,n=12^a,(m+n)=16^am/n=9^a/12^a=3^a/4^a(m+n)/n=16^a/12^a=4^a/3^a=1+m/n=1+3^a/4^a令m/n=t,则1+t=1/t===>t=(-1±√5)/2我想问一下t是怎样求出来的?
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![n满足方程log9(m)=log12(n)=log16(m+n),求n/m设Log9m=log12n=log16(m+n)=athen m=9^a,n=12^a,(m+n)=16^am/n=9^a/12^a=3^a/4^a(m+n)/n=16^a/12^a=4^a/3^a=1+m/n=1+3^a/4^a令m/n=t,则1+t=1/t===>t=(-1±√5)/2我想问一下t是怎样求出来的?](/uploads/image/z/7130134-46-4.jpg?t=n%E6%BB%A1%E8%B6%B3%E6%96%B9%E7%A8%8Blog9%28m%29%3Dlog12%28n%29%3Dlog16%28m%2Bn%29%2C%E6%B1%82n%2Fm%E8%AE%BELog9m%3Dlog12n%3Dlog16%28m%2Bn%29%3Dathen+m%3D9%5Ea%2Cn%3D12%5Ea%2C%28m%2Bn%29%3D16%5Eam%2Fn%3D9%5Ea%2F12%5Ea%3D3%5Ea%2F4%5Ea%28m%2Bn%29%2Fn%3D16%5Ea%2F12%5Ea%3D4%5Ea%2F3%5Ea%3D1%2Bm%2Fn%3D1%2B3%5Ea%2F4%5Ea%E4%BB%A4m%2Fn%3Dt%2C%E5%88%991%2Bt%3D1%2Ft%3D%3D%3D%3Et%3D%28-1%C2%B1%E2%88%9A5%29%2F2%E6%88%91%E6%83%B3%E9%97%AE%E4%B8%80%E4%B8%8Bt%E6%98%AF%E6%80%8E%E6%A0%B7%E6%B1%82%E5%87%BA%E6%9D%A5%E7%9A%84%3F)
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