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  • The equation  <img alt="\large \text { } x^2-4 x+[x]+3=x[x] \text {, where }[x] \text { : }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Clarge%20%5Ctext%20%7B%20%7D%20x%5E2-4%20xa

The equation  \large \text { } x^2-4 x+[x]+3=x[x] \text {, where }[x] \text { : } denotes the greatest integer function, has

Option: 1

a unique solution in (-\infty, 1)


Option: 2

no solution


Option: 3

exactly two solutions in (-\infty, \infty)


Option: 4

a unique solution in (-\infty, \infty)


Answers (1)

best_answer

\begin{aligned} & x^2-4 x+[x]+3=x[x] \\ & x^2-4 x+3=(x-1)[x] \\ & (x-1)(x-3)=(x-1)[x] \\ & x=1\;\;\;\; \text { or }\;\;\;\;\;\;\;x-3=[x] \\ &\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \mathrm{x}-[\mathrm{x}]=3 \\ &\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \{x\}=3 \\ & \end{aligned}

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Pankaj Sanodiya

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