1.

The solution set of equation `(x+2)^(2)+[x-2]^(2)=(x-2)^(2)+[x+2]^(2)`, where [.] represents the greatest integer function, isA. NB. ZC. QD. R

Answer» Correct Answer - B
We have,
`[x+n]=[x]+n` where `n in Z` and `x in R`.
`:. (x+2)^(2)+[x-2]^(2)=(x-2)^(2)+[x+2]^(2)`
`implies (x+2)^(2)-(x-2)^(2)=[x+2]^(2)-[x-2]^(2)`
`implies(x+2)^(2)-{(x+2)-4}^(2)=[x+2]^(2)-[(x+2)-4]^(2)`
`implies (x+2)^(2)-{(x+2)-4}^(2)=[x+2]^(2)-{[x+2]-4}^(2)`
`implies 8(x+2)=8[x+2]`
`implies(x+2)-[x+2]=0`
`implies {x+2}=0` , where{x} denotes the fractional part of x
`implies x+2 in Z implies x in Z`
Hence, the solution set of the given equation is the set ofintegers.


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