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Solution-of-equation-2-x-4-x-3x-2-where-denotes-fractional-function-and-denotes-G-I-F-is-1-2-2-2-3-2-3-4-R-

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Question Number 16082 by Tinkutara last updated on 17/Jun/17
Solution of equation 2[x] + 4{x} = 3x + 2 (where {∙} denotes fractional function and [∙] denotes G.I.F) is (1) {−2} (2) {−2, − (3/2)} (3) φ (4) R
Solutionofequation2[x]+4{x}=3x+2(where{⋅}denotesfractionalfunctionand[⋅]denotesG.I.F)is(1){−2}(2){−2,−32}(3)ϕ(4)R
Commented by Tinkutara last updated on 17/Jun/17
I got x = −2. I have checked that it satisfies the equation. But answer given in my book is φ. How is it possible?
Igotx=−2.Ihavecheckedthatitsatisfiestheequation.Butanswergiveninmybookisϕ.Howisitpossible?
Commented by prakash jain last updated on 17/Jun/17
x=[x]+{x} 2[x]+4{x}=3[x]+3{x}+2 [x]={x}−2 0≤{x}<1 [x] and 2 are integers so {x}=0 [x]=−2 ⇒x=−2 this is the only solutiin.
x=[x]+{x}2[x]+4{x}=3[x]+3{x}+2[x]={x}−20⩽{x}<1[x]and2areintegersso{x}=0[x]=−2⇒x=−2thisistheonlysolutiin.

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