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Solve : [x]^(2)=x+2{x}, where [.] and {....

Solve : `[x]^(2)=x+2{x},` where [.] and {.} denote the greatest integer and the fractional part functions, respectively.

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To solve the equation \([x]^2 = x + 2\{x\}\), where \([x]\) is the greatest integer function and \(\{x\}\) is the fractional part function, we can follow these steps: ### Step 1: Understand the Definitions Recall that: - \([x] = n\) (the greatest integer less than or equal to \(x\)) - \(\{x\} = x - [x] = x - n\) (the fractional part of \(x\)) ### Step 2: Rewrite the Equation ...
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