Question

Exercise 6 A number y satisfies y²⁴ - 256 = 0. What equation does the number x = y satisfy?

A. x⁴ - 16 = 0
B. x²⁴ - 256 = 0
C. x⁸ - 32 = 0
D. x⁶ - 64 = 0

Answer 1

Given the equation y²⁴ - 256 = 0, the equivalent equation for x = y is x⁶ - 64 = 0, which aligns with option D.

Step-by-step explanation:

The given equation is y²⁴ - 256 = 0. To find a related equation for x = y, we look for a transformation that simplifies the expression. Taking the fourth root on both sides of the original equation gives us y⁶ - 4 = 0. Replacing y with x since they are equal, the equation that x satisfies is x⁶ - 64 = 0, which corresponds to option D.