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What are all the real zeroes of y=(x–12)^3–7
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To find the real zeros of the equation y=(x–12)^3–7, we need to find the values of x that make y equal to zero.
Setting y equal to zero, we have 0=(x–12)^3–7.
Adding 7 to both sides, we get (x–12)^3 = 7.
To solve for x, we will take the cube root of both sides. However, it's important to note that the cube root has three possible solutions: one real and two complex. Since we are looking for real zeros, we will only consider the real cube root.
∛((x–12)^3) = ∛7.
Taking the cube root of both sides, we have x–12 = ∛7.
Now, adding 12 to both sides, we get x = 12 + ∛7.
Therefore, the only real zero of the equation is x = 12 + ∛7.