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If open curly brackets x close curly brackets and open square brackets x close square brackets respectively denote the fractional and integral parts of the real number x then number of real roots of the equation open curly brackets bold x bold plus bold 1 close curly brackets bold plus bold 2 bold italic x bold equals bold 4 open square brackets bold x bold plus bold 1 close square brackets bold minus bold 6 bold spaceis:- (A) 4            (B) 3          (C) 1        (D) 2 (Please write detail answer for this question)
Asked by Tech guides by | 21 Jun, 2019, 05:50: PM
answered-by-expert Expert Answer
{x+1}+2x=4[x+1]-6
{x}+2x=4([x]+1)-6  ..... (Since excluding integral part i.e. 1 from {x+1} won't affect the result as it is fractional part and [x+1]=[x]+1)
x-[x]+2x=4[x]+4-6
3x=5[x]-2
3x+2=5[x]
rightwards double arrow left square bracket x right square bracket equals fraction numerator 3 x plus 2 over denominator 5 end fraction S o comma space 3 x plus 2 space m u s t space b e space a space m u l t i p l e space o f space 5 space i. e. space 3 x space m u s t space b e space 3 comma space 8 comma space 13 comma space 18 comma space 23 comma space 28 comma space 33 comma space a n d space s o space o n. left square bracket x right square bracket equals fraction numerator 3 x plus 2 over denominator 5 end fraction space i s space p o s s i b l e space o n l y space w h e n space x equals 1 T h u s comma space t h e space r o o t space o f space t h e space e q u a t i o n space left curly bracket x plus 1 right curly bracket plus 2 x equals 4 left square bracket x plus 1 right square bracket minus 6 space i s space 1. H e n c e comma space t h e space n u m b e r space o f space r o o t s space i s space 1.
Answered by Renu Varma | 26 Jun, 2019, 03:26: PM

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