The solution of x−$$1=(x$$−[x]$$)(x$$−$${x})$$ (where$$ [x] and $${x}$$ are the integral and fractional part of x $$) is :

Question

The solution  of x−$$1=(x$$−[x]$$)(x$$−$${x})$$      (where$$ [x]      and $${x}$$      are the integral and  fractional part of x     $$) is :

Infinity Learn · Accepted Answer

∵                (x$$−$$1)=(x$$−[x]$$)(x$$−$${x})       ⇒                $$x=1+{x}$$[x]     ⇒              [x]$$+{x}=1+{x}$$[x]     ⇒              $$({x}$$−$$1)($$[x]−$$1)=0$$              $${x}$$−$$1$$≠$$0$$,      ∴    [x]−$$1=0$$                    [x]$$=1$$    ⇒x∈[$$1$$,$$2)$$

The solution of $x - 1 = (x - [x]) (x - {x})$ (where $[x]$ and ${x}$ are the integral and fractional part of $x$ ) is :

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The solution of x−1=(x−[x])(x−{x}) (where [x] and {x} are the integral and fractional part of x ) is :

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The solution of $x - 1 = (x - [x]) (x - {x})$ (where $[x]$ and ${x}$ are the integral and fractional part of $x$ ) is :