input for y=cubed root of -y+3 when the output is 2

The equation you provided is:

\[
y = \sqrt[3]{-y + 3}
\]

You mentioned that the output is \(2\), meaning when \(y = 2\), the equation should hold true. Let's substitute \(y = 2\) into the equation and solve for verification.

\[
2 = \sqrt[3]{-2 + 3}
\]

\[
2 = \sqrt[3]{1}
\]

Since the cube root of \(1\) is \(1\), the equation doesn't hold true for \(y = 2\). It seems like the value for \(y\) needs to be recalculated or reassessed. Would you like me to solve the equation \(y = \sqrt[3]{-y + 3}\) and find a correct value for \(y\)?

Here are a few questions related to the topic:

1. Would you like a step-by-step breakdown of solving the equation?
2. Would you like to explore graphical methods to verify solutions?
3. Do you want to learn more about cube roots of negative numbers?
4. How can we use iteration methods to solve this kind of equation?
5. Would you like me to explain how to check the domain of such equations?

**Tip:** When solving equations involving cube roots, remember that the cube root of a negative number exists and is negative, unlike square roots where the number must be positive.

Explore how to solve the cube root equation y = ∛(-y + 3) when y = 2 doesn't hold true. This problem covers key algebraic concepts involving cube roots and verification of solutions. Ideal for students in Grades 9-12, it offers insights into solving cube root equations and understanding cube root properties.

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