lgX/10乘以lgX2/10等于3的方程怎么解

题目

lgX/10乘以lgX2/10等于3的方程怎么解

答案

lgX2/10=lg(X²/10)?
lg(X/10)[lg(X²/10)]=3
(lgX-lg10)[lg(X²)-lg10]=3
(lgX-1)(2lgX-1)=3
2(lgX)²-3lgX+1-3=0
2(lgX)²-3lgX-2=0
lgX={3±√[(-3)²-4×2×(-2)]}/(2×2)
=[3±√(9+16)]/4=(3±5)/4
lgX=(3+5)/4=2,X1=10²=100;
lgX=(3-5)/4=-1/2,X2=10^(-1/2)=1/[√(10)]=√(10)/(10);