Question

$A=\{x:x\in R,x^2=16\text{and}2x=6\}$. Represent the set in roster form.

Answer 1

Given $A=\{x:x\in R,x^2=16\text{and}2x=6\}$

$A$ is the set of common solutions of equations $x^2=16\text{and}2x=6$.
Solution of $x^2=16\Rightarrow x=\pm 4$
Solution of $2x=6\Rightarrow x=3$

There is no value of $x$ which satisfies both the given equations.

Therefore the set $A$ is an empty set or a null set.

Thus, $A=\left\{\right\}$.