If x∈R satisfies (log10100x)2+(log1010x)2+log10x≤14 then x contains the interval
(0,10)
Writing u=log10x, the given inequality can be written as (2+u)2+(1+u)2+u≤14⇒2u2+7u−9≤0⇒(2u+9)(u−1)≤0⇒−92≤u≤1⇒−92≤log10x≤1⇒10−92≤x≤10