Question

解方程：9^x+6^x=2^2x+1

Answer 1

9^x+6^x=2^2x+1
9^x+6^x=2*4^x
(9/4)^x+(6/4)^x=2
令a=(3/2)^x
则a²+a-2=0
(a+2)(a-1)=0
显然a>0
所以a=1
(3/2)^x=1
x=0

Answer 2

x+y>=2√xy
所以(x+y)2>=4xy
xy<=(x+y)2/4

xy=(x+y)+1<=(x+y)2/4
令a=x+y
即a2>=4a+4
a2-4a-4>=0
a<=2-2√2,a>=2+2√2
a=x+y>0
所以x+y>=2+2√2