Question 19

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

The equation x² - 10 = 0 can be solved by isolating x², which leads to x² = 10. Taking the square root of both sides results in x = ±√(10).

A) ±5

This option is incorrect because if x were ±5, then x² would equal 25, not 10. Therefore, ±5 does not satisfy the equation x² - 10 = 0.

B) ±√(10)

This option is correct as solving the equation x² - 10 gives us x² = 10, leading to the solutions x = ±√(10). This directly satisfies the equation.

C) ±10

This option is incorrect because if x were ±10, then x² would equal 100, not 10. Thus, ±10 does not satisfy the equation x² - 10 = 0.

D) ±10²

This option is incorrect as ±10² equals ±100, which does not solve the equation x² - 10 = 0. Therefore, it does not provide the correct solutions.

E) ±20

This option is also incorrect because if x were ±20, then x² would equal 400, which does not satisfy the equation x² - 10 = 0.

Conclusion

The correct answer, ±√(10), is the only solution that accurately resolves the equation x² - 10 = 0. All other options provide values that do not satisfy the equation, confirming that they are incorrect.