Rationale
±√(10) are the solutions to the equation x²-10.
To solve the equation x² - 10 = 0, we isolate x² to get x² = 10, and then take the square root of both sides, which yields the solutions ±√(10).
A) The choice ±5 suggests that the equation x² = 25 is being considered, which is incorrect. The original equation x² - 10 = 0 leads to x² = 10, not 25, making ±5 an inaccurate solution for the given equation.
B) This is the correct choice as it accurately represents the solutions derived from the equation x² = 10. By taking the square root of both sides, we find that x = ±√(10), confirming these values satisfy the original equation.
C) The choice ±10 implies that the equation x² = 100 is under consideration. However, the original equation is x² - 10 = 0, leading to x² = 10, thus ±10 does not satisfy the equation.
D) The choice ±10² indicates a misunderstanding of the solution process. While 10² equals 100, it does not relate to the equation x² - 10 = 0, which does not involve squaring the solutions.
E) The choice ±20 suggests a misinterpretation of the quadratic equation entirely; it implies x² = 400, which is unrelated to the correct equation. The solution x² = 10 leads to ±√(10), making ±20 incorrect.
Conclusion
The solutions to the equation x² - 10 = 0 are ±√(10), as derived from isolating x² and taking the square root. Other choices either misinterpret the equation or suggest unrelated values that do not satisfy the original quadratic. Understanding the correct approach to solving quadratic equations is crucial for identifying valid solutions.