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Equation of a Plane : Intercept Form

If x represen...

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If {x} represents the least integer, not less than x, then total number of solutions of the equation (x−1)2+{x}=4, is equal to

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R =

the set of real numbers,

Z =

the set of integers,

N =

the set of natural numbers. If

S

be the solution set of the equation

(x)^{2} + [x]^{2} = (x - 1)^{2} + [x + 1]^{2},

(x) =

the least integer greater than or equal to

x

[x] =

the greatest integer less than or equal to

x

Q. The solution of the equation

2 x - 2 [x] = 1

[x]

represents greatest integer function less than or equal to

x

Q. The period of

sin \frac{π [x]}{12} + cos \frac{π [x]}{4} + tan \frac{π [x]}{3}

[x]

represents the greatest integer less than or equal to

x

Q. The solution set of the equation

[2 x] = [x] + 3, 0 \leq x \leq 4

[x] =

the greatest integer less than or equal to

x

Q. Solve the equation

{(x)}^{2} = {[x]}^{2} + 2 x

when [x] and (x) are the integer just less than or equal to x and just greater than or equal to x respectively.
find the number of integral solutions

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