Let `[a]` denotes the larger integer not exceeding the real number `a` if `x` and `y` satisfy the equations `y=2[x]+3` and `y=3[x-2[` simultaneously d

Question

Let `[a]` denotes the larger integer not exceeding the real number `a` if `x` and `y` satisfy the equations `y=2[x]+3` and `y=3[x-2[` simultaneously d

Let `[a]` denotes the larger integer not exceeding the real number `a` if `x` and `y` satisfy the equations `y=2[x]+3` and `y=3[x-2[` simultaneously determine `[x+y]`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

We have `y=2[x]+3=3[x-2]`……i ltbr `implies2[x]+3=3([x]-2)`[from property (i)]
`implies2[x]+3=3[x]-6`
`implies[x]=9`
From Eq. (i) `y=2xx9+3=21`
`:.[x+y]=[x+21]=[x]+21=9+21=30`
hence the value of `[x+y]` is 30.

4 views Answered 2023-02-05 15:29