Question Number 16087 by Tinkutara last updated on 17/Jun/17
![Number of solution of equation 2[−x] + 3x = 7{x} is? (where [∙] = Greatest Integer Function & {∙} fractional function.)](https://www.tinkutara.com/question/Q16087.png)
$$\mathrm{Number}\:\mathrm{of}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{equation} \\ $$$$\mathrm{2}\left[−{x}\right]\:+\:\mathrm{3}{x}\:=\:\mathrm{7}\left\{{x}\right\}\:\mathrm{is}?\:\left(\mathrm{where}\:\left[\centerdot\right]\:=\right. \\ $$$$\mathrm{Greatest}\:\mathrm{Integer}\:\mathrm{Function}\:\&\:\left\{\centerdot\right\} \\ $$$$\left.\mathrm{fractional}\:\mathrm{function}.\right) \\ $$
Commented by prakash jain last updated on 17/Jun/17
![x=[x]+{x} 2[−x]+3[x]+3{x}=7{x} 4{x}=2[−x]+3[x] RHS integer {x}=0 {x}=0⇒x=n 2[−n]+3[n]=0 ⇒n=0 x=0](https://www.tinkutara.com/question/Q16100.png)
$${x}=\left[{x}\right]+\left\{{x}\right\} \\ $$$$\mathrm{2}\left[−{x}\right]+\mathrm{3}\left[{x}\right]+\mathrm{3}\left\{{x}\right\}=\mathrm{7}\left\{{x}\right\} \\ $$$$\mathrm{4}\left\{{x}\right\}=\mathrm{2}\left[−{x}\right]+\mathrm{3}\left[{x}\right] \\ $$$$\mathrm{RHS}\:{integer}\:\left\{{x}\right\}=\mathrm{0} \\ $$$$\left\{{x}\right\}=\mathrm{0}\Rightarrow{x}={n} \\ $$$$\mathrm{2}\left[−{n}\right]+\mathrm{3}\left[{n}\right]=\mathrm{0} \\ $$$$\Rightarrow{n}=\mathrm{0} \\ $$$${x}=\mathrm{0} \\ $$