for what value of x {x=x^2;x belongs to R}

for that your answer is

We have, *x* ^{2 } = *x* ⇒ * x* ^{2 } - *x* = 0 ⇒ *x* ( *x * - 1) = 0 ⇒ * x* = 0 or 1

So there are two values of *x *that is 0 and 1 as both of them belongs to R

What if we take 1=x/x^2 and if we substitute x=0 then it becomes 1/0 which is undefined.

Please explain why x=0

The equation* x*^{2 }= *x* is considered as an quadratic equation, which is simplified by the method given below

*x*^{2 }= *x ⇒ x*^{2 }- *x = *0 ⇒ *x* (*x* - 1) = 0 ⇒* x *= 0 or *x* = 1

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