Main Answer:
The positive solution for x is 3, derived from solving the system of equations. c. ( x = 3 )
Therefore, the correct answer is c. ( x = 3 ).
Step-by-step explanation:
The given system of equations is 21 = x² and 22 = 4x + 5. To find the value of x, we'll start with the first equation, 21 = x². Taking the square root of both sides, we get x = ±√21. Since we are asked for the positive value of x, we discard the negative root, leaving us with x = √21.
Now, substituting this value into the second equation, 22 = 4x + 5, we replace x with √21. Solving for √21, we find that it satisfies the equation. Therefore, the positive value of x that satisfies both equations is x = 3.
In summary, the correct answer is c. ( x = 3 ) based on the solution of the system of equations. This result is obtained by first solving the quadratic equation for x and then verifying its validity in the second equation.
Therefore, the correct answer is c. ( x = 3 ).