Question

Set f(y) equal to g(y) and solve for y ⇒ y³⁶ - y² = ⇒ y =

a) y = 1
b) y = 0
c) y = -1
d) y = ±1

Answer 1

The equation y³⁶ - y² = 0 has three solutions: y = 0, y = 1, and y = -1. These solutions are determined by factoring out y² and setting each factor equal to zero.

Step-by-step explanation:

To solve the equation f(y) = g(y), given as y³⁶ - y² = 0, we first factor out the common term of y². The factored form of the equation is y²(y³⁴ - 1) = 0. Setting each factor equal to zero gives us the potential solutions y = 0 and y³⁴ - 1 = 0. The second equation simplifies to y³⁴ = 1, which implies that y = 1 or y = -1, since 1 and -1 are the only real numbers that raised to any even power give 1.

Therefore, the solutions are y = 0, y = 1, and y = -1. These correspond to answer options (b), (a), and (c) respectively. Option (d) y = ±1 is not a separate solution but collectively refers to both (a) and (c).