解不等式x^3-3log2(x)-[log2(x)]^2-1/8x^2>0解不等式x^3-3log2(x)-[log2(x)]^2-1/8x^2>0我把log2(x)=t原式子=x^3-3t-t^2-1/8x^2>0

Question

解不等式x^【3-3log2(x)-[log2(x)]^2】-1/8x^2>0
解不等式x^【3-3log2(x)-[log2(x)]^2】-1/8【x^2】>0
我把log2(x)=t
原式子=
x^【3-3t-t^2】-1/8【x^2】>0

Answer 1

log2(x)=t x=2^t
原式=(2^t)^(3-3t-t^2)-1/8*(2^t)^2=2^(3t-3t^2-t^3)-2^(-3)*2^2t=2^(3t-3t^2-t^3)-2^(2t-3)>0
因为2^x是增函数,只需
3t-3t^2-t^3>2t-3即可,即 t^3+3t^2-t-3