Q14 Dante, Ahmed and Olivia are discussing the solution set to the equation x2+16=25

Question

Dante says the solution is {3}
Ahmed says the solution is {-3, 3}
Olivia says the solution is {-3}
Which person has found the correct solution set?
Dante
Ahmed
Olivia
None of them are correct

Answer 1

To solve the equation \( x^2 + 16 = 25 \), we first isolate \( x^2 \):

\[ x^2 = 25 - 16 \] \[ x^2 = 9 \]

Now, we take the square root of both sides:

\[ x = 3 \quad \text{or} \quad x = -3 \]

Thus, the solution set is \( {-3, 3} \).

Now we can evaluate the answers given by Dante, Ahmed, and Olivia:

• Dante says the solution is \( {3} \) (Incorrect)
• Ahmed says the solution is \( {-3, 3} \) (Correct)
• Olivia says the solution is \( {-3} \) (Incorrect)

Therefore, the correct answer is Ahmed.