解方程 6的X次方＋4的X次方＝9的X次方,求x的值?

题目

解方程 6的X次方＋4的X次方＝9的X次方,求x的值?

答案

6^x+4^x = 9^x两边同除以9^x,可得：(2/3)^x+(2/3)^(2x) = 1 ,令 y = (2/3)^x ,可得：y+y^2 = 1 ,即：y^2+y-1 = 0 ,解得：y = (√5-1)/2 ,（舍去负值）即：(2/3)^x = (√5-1)/2 ,可得：x = log(2/3)[(√5-1)/2] ....