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{:[x=1 Longrightarrowx^(r)=x],[ Longrightarrowx^(r)-x=0],[ Longrightarrow x(x-1)=0],[ Longrightarrow(x(x-1))/(x-1)=(@)/(x-1)],[ Longrightarrow x=0],[ Longrightarrow1=0.]:}

x=1amp;⟹xr=xamp;⟹xr−x=0amp;⟹x(x−1)=0amp;⟹x(x−1)x−1=∘x−1amp;⟹x=0amp;⟹1=0. \begin{aligned} x=1 & \Longrightarrow x^{r}=x \\ & \Longrightarrow x^{r}-x=0 \\ & \Longrightarrow x(x-1)=0 \\ & \Longrightarrow \frac{x(x-1)}{x-1}=\frac{\circ}{x-1} \\ & \Longrightarrow x=0 \\ & \Longrightarrow 1=0 .\end{aligned}

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Q. x=1⟹xr=x⟹xr−x=0⟹x(x−1)=0⟹x(x−1)x−1=∘x−1⟹x=0⟹1=0. \begin{aligned} x=1 & \Longrightarrow x^{r}=x \\ & \Longrightarrow x^{r}-x=0 \\ & \Longrightarrow x(x-1)=0 \\ & \Longrightarrow \frac{x(x-1)}{x-1}=\frac{\circ}{x-1} \\ & \Longrightarrow x=0 \\ & \Longrightarrow 1=0 .\end{aligned}
  1. Explanation of x=1x=1: Look at the first step x=1x=1 implies xr=xx^{r}=x. This is true because any number raised to the power of rr, where rr is the real number, equals the number itself when the number is 11.
  2. Derivation of xr−x=0x^{r}-x=0: Move to the next step xr−x=0x^{r}-x=0. This follows from the previous step since xr=xx^{r}=x, subtracting xx from both sides gives 00.
  3. Factorization of x(x−1)=0x(x-1)=0: The next step is x(x−1)=0x(x-1)=0. This is a factoring of the previous equation, which is correct.
  4. Error in dividing by (x−1)(x-1): The step x(x−1)x−1=@x−1\frac{x(x-1)}{x-1}=\frac{@}{x-1} is next.\newlineHere, we have a mistake. Dividing by (x−1)(x-1) is not allowed when x=1x=1 because it results in division by zero, which is undefined.

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