Square Roots

We are asked to solve the following system of linear equations for and :
Equation 1:
Equation 2:

We can use the method of elimination. Let's eliminate .
Multiply Equation 1 by :

--- (Equation 3)

Multiply Equation 2 by :

--- (Equation 4)

Now, add Equation 3 and Equation 4:



Divide both sides by 5:

Substitute the value back into Equation 1:



Simplify : .

Subtract from both sides:


Divide both sides by :

So, the correct option is (B):

We are given the equation: Multiply both sides by to eliminate the denominator: Rearrange the terms to form a quadratic equation: Now solve for using the quadratic formula: So, the roots are:

The correct option is (C):

We are tasked with finding the value of , where is a common root of the equations and .

Step 1: Substitute into both equations.

For the first equation :

For the second equation :

Step 2: Compute .

Final Answer: The value of is , which corresponds to option .