Let $$3\leq x\leq6$$ and $$\left[x^{2}\right] =\left[x\right]^{2}$$ , where $$[x]$$ is the greatest integer no

Question

Let $$3\leq x\leq6$$ and $$\left[x^{2}\right] =\left[x\right]^{2}$$ , where $$[x]$$ is the greatest integer not exceeding $$x$$ . If set $$S$$ represents all feasible values of $$x$$, then a possible subset of $$S$$ is

Accepted Answer

( 3 , 10 ) ∪ [ 5 , 26 ) ∪ { 6 } \left(3,\sqrt{10}\right)\cup \left[5,\sqrt{26}\right)\cup \left\{6\right\} ( 3 , 10 ​ ) ∪ [ 5 , 26 ​ ) ∪ { 6 }. For n=3,4,5 and x ∈ [ n , n + 1 ) x\in[n,n+1) x ∈ [ n , n + 1 ) we have ⌊ x ⌋ = n \lfloor x\rfloor=n ⌊ x ⌋ = n , so the equation ⌊ x 2 ⌋ = ⌊ x ⌋ 2 = n 2 \lfloor x^2\rfloor=\lfloor x\rfloor^2=n^2 ⌊ x 2 ⌋ = ⌊ x ⌋ 2 = n 2 x 2 ∈ [ n 2 , n 2 + 1 ) x^2\in[n^2,n^2+1) x 2 ∈ [ n 2 , n 2 + 1 ) , i.e. x ∈ [ n

Let $3\leq x\leq6$ and $\left[x^{2}\right] =\left[x\right]^{2}$ , where $[x]$ is the greatest integer not exceeding $x$ . If set $S$ represents all feasible values of $x$ , then a possible subset of $S$ is

Let $3\leq x\leq6$ and $\left[x^{2}\right] =\left[x\right]^{2}$ , where $[x]$ is the greatest integer not exceeding $x$ . If set $S$ represents all feasible values of $x$ , then a possible subset of $S$ is

Let 3≤x≤63\leq x\leq63≤x≤6 and [x2]=[x]2\left[x^{2}\right] =\left[x\right]^{2}[x2]=[x]2 , where [x][x][x] is the greatest integer not exceeding xxx . If set SSS represents all feasible values of xxx, then a possible subset of SSS is

Let 3≤x≤63\leq x\leq63≤x≤6 and [x2]=[x]2\left[x^{2}\right] =\left[x\right]^{2}[x2]=[x]2 , where [x][x][x] is the greatest integer not exceeding xxx . If set SSS represents all feasible values of xxx, then a possible subset of SSS is

Let $3\leq x\leq6$ and $\left[x^{2}\right] =\left[x\right]^{2}$ , where $[x]$ is the greatest integer not exceeding $x$ . If set $S$ represents all feasible values of $x$ , then a possible subset of $S$ is

Let $3\leq x\leq6$ and $\left[x^{2}\right] =\left[x\right]^{2}$ , where $[x]$ is the greatest integer not exceeding $x$ . If set $S$ represents all feasible values of $x$ , then a possible subset of $S$ is