4a^2+9b^2=13
3b-2a=-5
(3b-2a)^2=(-5)^2
4a^2-12ab+9b^2=25
13-12ab=25
ab=-1
2a^(2n+4)[b^(2n+3)+3b^(2n+5)/2]
=2a^(2n+4)b^(2n+3)+3a^(2n+4)b^(2n+5)
=2a*[a^(2n+3)b^(2n+3)]+3b[a^(2n+4)b^(2n+4)]
=2a*(ab)^(2n+3)+3b*(ab)^(2n+4)
=2a*(-1)^(2n+3)+3b*(-1)^(2n+4)
因为2n+3是奇数,2n+4是偶数
所以(-1)^(2n+3)=-1,(-1)^(2n+4)=1
所以原式=2a*(-1)+3b*1
=3b-2a=-5