Question

4的x次方加6的x次方等于9的x次方

Answer 1

4^x+6^x=9^x

(4/6)^x+1=(9/6)^x

(2/3)^x+1=(3/2)^x

((2/3)^x)^2+(2/3)^x-1=0

设(2/3)^x=a

则：a^2+a-1=0,a>0

a=(√5-1)/2

即：(2/3)^x=(√5-1)/2

x=log(2/3)[(√5-1)/2]