Question

If a+b+c=abc then how many real number solutions are possible?
A). Unique solution
B). No Solution C). Two Solutions
D). Infinite Solutions

Answer 1

Hint: According to the question, we are having an equation of three variables and we need to find the number of real valued solutions of this equation. Now, we know that by real value we mean that if we get any complex root then we don’t need to count that as only roots that are real are to be counted.

Complete step-by-step solution:
In the given question, we are given an equation in three variables and we are asked about the number of real valued solutions of the equation. Now, we know that to get the independent solution of three variable equations we need three equations.
As per the question we have only one equation. SO, we can clearly say that we can’t get different values of different variables independently. Therefore, the solution of the given equation will be dependent on each other. Therefore, we have infinitely many real valued solutions for the given equation.
Hence, the number of real valued solutions of the equation $a+b+c=abc$ is infinitely many. So option D is the correct option.

Note: In such types of questions, we need to get the concept of solutions and equations just by visualizing rather than just starting solving them as we know various ways by which we can tell whether the given equation will have unique, no or infinite roots. Also, we need to relate the number of equations with the number of variables and identify.