For any two real numbers x- y if 4- x-5 and 5- y-6- then the range of -x-y-

Given: Two real numbers x, y and 4≤ x lt;5 ⇒ [x]=4⋯(i) Similarly, 5≤ y lt;6⇒ [y]=5 nbsp; Now, we know the relation: [x]+[y]≤ [x+y]≤ [x]+[y]+1 ⇒ 4+5≤ [x+y] ...

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For any two r...

Question

For any two real numbers $x, y$ if $4 \leq x < 5$ and $5 \leq y < 6,$ then the range of $[x + y] \in$

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Solution

Given: Two real numbers $x, y$ and
$4 \leq x < 5 \Rightarrow [x] = 4 \dots (i)$
Similarly, $5 \leq y < 6 \Rightarrow [y] = 5$
Now, we know the relation:
$[x] + [y] \leq [x + y] \leq [x] + [y] + 1 \Rightarrow 4 + 5 \leq [x + y] \leq 4 + 5 + 1 \Rightarrow [x + y] \in [9, 10]$
But since $[x + y]$ is always an integer
$∴ [x + y] \in {9, 10}$

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For any two real numbers x,y if 4≤x<5 and 5≤y<6, then the range of [x+y]∈

Given: Two real numbers x,y and 4≤x<5⇒[x]=4⋯(i) Similarly, 5≤y<6⇒[y]=5 Now, we know the relation: [x]+[y]≤[x+y]≤[x]+[y]+1⇒4+5≤[x+y]≤4+5+1⇒[x+y]∈[9,10] But since [x+y] is always an integer ∴[x+y]∈{9,10}

For any two real numbers $x, y$ if $4 \leq x < 5$ and $5 \leq y < 6,$ then the range of $[x + y] \in$