Aspire Faculty ID #13835 · Topic: JAMIA MILLIA ISLAMIA MCA 2021 · Just now
JAMIA MILLIA ISLAMIA MCA 2021

If $[x^2] - 5[x] + 6 = 0$, where $[\,]$ denotes the greatest integer function, then

Solution

Let $[x] = n$. Then $[x^2] = n^2$ (since $x^2$ lies between $n^2$ and $(n+1)^2$). Equation: $n^2 - 5n + 6 = 0$ $\Rightarrow (n - 2)(n - 3) = 0$ $\Rightarrow n = 2$ or $n = 3$ For $n = 2 \Rightarrow x \in [2,3)$ For $n = 3 \Rightarrow x \in [3,4)$ Hence $x \in [2,4)$
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