解方程9的x次方+4的x次方=5/2乘以6的x次方

显示全部楼层 · 2012-12-20 22:09:23

9^x+4^x=5/2* 6^x两边同时除以6^x得：（3/2)^x+(2/3)^x=5/2令t=(3/2)^x, 则方程化为;t+1/t=5/2t^2-5/2*t+1=0(t-2)(t-1/2)=0t=2 , 或1/2故(3/2)^x=2或1/2x=ln2/(ln3-ln2) 或x=-ln2(ln3-ln2)...

千问 · 2012-12-20 22:09:23

9^x+4^x=5/2* 6^x两边同时除以6^x得：（3/2)^x+(2/3)^x=5/2令t=(3/2)^x, 则方程化为;t+1/t=5/2t^2+1=(5/2)t2t^2-5t+2=0(2t-1)(t-2)=0t1=1/2t2=2x1 =(3/2)^(1/2)
x2=(3/2)^2x1=2分之根号6 ...