Question

方程lg2x*lg3x+a^2=0有两个相异的实数根,求实数a的取值范围

Answer 1

lg2x)(lg3x)=-a^2

===> (lgx+lg2)(lgx+lg3)+a^2 = 0

==> (lgx)^2 + (lg2+lg3)lgx + (a^2+lg2lg3) = 0.(1)

方程(lg2x)(lg3x)=-a^2有两个相异实数解

则(1)的判别式=(lg2+lg3)^2 - 4*(a^2+lg2lg3) > 0

化简,得:-lg(3/2)/2 < a < lg(3/2)/2

不懂再问哦