If - x - x - x - x - x -10- then x lies inA- -10-11B- -5-6 - -2-3D- Z

The correct option is C [2,3)[x+[x+[x+[x+[ x]]]]]=10 As [x+ℤ]=[x]+ℤ, so ⇒[x+[x]]=[x]+[x] So, [x+[x+[x+[x+[ x]]]]]=10 ⇒ [x]+[x]+[x]+[x]+[x]=10 ⇒ 5[x]=10 ⇒ [x]=2 ...

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Byju's Answer

Standard XII

Mathematics

Greatest Integer Function

If [ x +[ x +...

Question

If $[x + [x + [x + [x + [x]]]]] = 10$ , then $x$ lies in

[10, 11)

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[2, 3)

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Z

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[5, 6)

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Solution

The correct option is B $[2, 3)$
$[x + [x + [x + [x + [x]]]]] = 10$
As $[x + Z] = [x] + Z$ , so
$\Rightarrow [x + [x]] = [x] + [x]$
So,
$[x + [x + [x + [x + [x]]]]] = 10 \Rightarrow [x] + [x] + [x] + [x] + [x] = 10 \Rightarrow 5 [x] = 10 \Rightarrow [x] = 2 \Rightarrow x = [2, 3)$

Suggest Corrections

If [x+[x+[x+[x+[x]]]]]=10, then x lies in

The correct option is B [2,3)[x+[x+[x+[x+[x]]]]]=10 As [x+Z]=[x]+Z, so ⇒[x+[x]]=[x]+[x] So, [x+[x+[x+[x+[x]]]]]=10⇒[x]+[x]+[x]+[x]+[x]=10⇒5[x]=10⇒[x]=2⇒x=[2,3)

If $[x + [x + [x + [x + [x]]]]] = 10$ , then $x$ lies in

The correct option is B $[2, 3)$
$[x + [x + [x + [x + [x]]]]] = 10$
As $[x + Z] = [x] + Z$ , so
$\Rightarrow [x + [x]] = [x] + [x]$
So,
$[x + [x + [x + [x + [x]]]]] = 10 \Rightarrow [x] + [x] + [x] + [x] + [x] = 10 \Rightarrow 5 [x] = 10 \Rightarrow [x] = 2 \Rightarrow x = [2, 3)$