Question

The value of \( x \) obtained from the equation \[ \frac{x + \alpha}{\gamma} = \frac{x + \beta}{\alpha} = \frac{x + \gamma}{\beta} \] will be

• A. \( x = \alpha + \beta + \gamma \)
• B. \( x = \alpha + \beta + \gamma \)
• C. \( x = \frac{1}{\alpha + \beta + \gamma} \)
• D. None of these

Hint:

When dealing with ratios, cross-multiply and simplify the equations to solve for the unknown variable.

Answer 1

The Correct Option is A

Step 1: Solve the given system of equations.
By solving the system of equations using basic algebraic methods, the value of \( x \) is found to be \( x = \alpha + \beta + \gamma \).
Step 2: Conclusion.
Thus, the value of \( x \) is \( \alpha + \beta + \gamma \).
Final Answer: \[ \boxed{x = \alpha + \beta + \gamma} \]