Question

已知5/x=3/y,求x+y/x+x-y/y-x^2-y^2/y^2的值

Answer 1

y=3x/5
所以原式=(x+3x/5)/x+(x-3x/5)/(3x/5)-(x^2-9x^2/25)/(9x^2/25)
=8/5+2/3-16/9
=22/45

Answer 2

bn/b(n-1)=√[a(n+1)a(n+2)]/√[ana(n+1)]=q
平方
a(n+2)=an*q^2

cn/c(n-1)
=[a(2n-1)+2a(2n)]/[a(2n-3)+2a(2n-2)]
a(2n-1)=a(2n-3)*q^2
a(2n)=a(2n-2)*q^2
所以cn/c(n-1)=q^2
所以cn是等比数列