Subjects algebra

Solve Cubic Linear Bc8757

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Solve Cubic Linear Bc8757


1. **State the problem:** Solve the equation $b \times b \times b = b + b + b$. 2. **Rewrite the equation:** The left side is $b^3$ (since $b \times b \times b = b^3$) and the right side is $3b$ (since $b + b + b = 3b$). 3. **Set up the equation:** $$b^3 = 3b$$ 4. **Bring all terms to one side:** $$b^3 - 3b = 0$$ 5. **Factor the equation:** $$b(b^2 - 3) = 0$$ 6. **Solve each factor:** - $b = 0$ - $b^2 - 3 = 0 \Rightarrow b^2 = 3 \Rightarrow b = \pm \sqrt{3}$ 7. **Final solutions:** $$b = 0, \quad b = \sqrt{3}, \quad b = -\sqrt{3}$$ These are the values of $b$ that satisfy the original equation.