What are the solutions to the equation x²-10?

Rationale

±√(10) are the solutions to the equation x²-10.

The equation x² - 10 = 0 can be solved by adding 10 to both sides and then taking the square root of both sides, leading to the solutions ±√(10). This indicates the values of x that satisfy the equation.

A (±5) YOUR ANSWER

This choice suggests that the solutions are ±5, which does not satisfy the original equation. Substituting 5 into the equation gives 5² - 10 = 25 - 10 = 15, which does not equal zero. Therefore, ±5 cannot be solutions to the equation.

B (±√(10)) CORRECT

This choice correctly represents the solutions to the equation. By solving x² - 10 = 0, we find that x = ±√(10) is the accurate resolution, as substituting these values back into the equation will yield zero.

C (±10) YOUR ANSWER

Selecting ±10 implies that the solutions to the equation are 10 and -10. However, substituting either of these values into the equation results in 10² - 10 = 100 - 10 = 90, which again does not satisfy the equation. Thus, ±10 are not valid solutions.

D (±10²) YOUR ANSWER

This option misrepresents the solutions by suggesting ±10² (which is ±100). Substituting 100 back into the equation gives 100² - 10 = 10000 - 10 = 9990, clearly not resolving to zero. Hence, this choice is incorrect.

E (±20) YOUR ANSWER

This choice suggests that the solutions are ±20. Substituting 20 into the equation results in 20² - 10 = 400 - 10 = 390, which does not equal zero. Therefore, ±20 cannot be considered as solutions.

Conclusion

The equation x² - 10 = 0 is accurately solved using the square root method, leading to the solutions ±√(10). Each incorrect option fails to satisfy the equation when substituted back, emphasizing that only ±√(10) correctly resolves the original expression to zero. This demonstrates the importance of correctly applying algebraic principles to find valid solutions.