Q: How do you get V = 3.34, 6.81 from the equation V³ = 80.3V − 231?
🔹 Step 1: Rewrite the Equation
The given equation is:
V³ = 80.3V − 231
Bring all terms to one side to form a standard cubic equation:
V³ − 80.3V + 231 = 0
🔹 Step 2: Recognize the Form
We now have a cubic equation in the form:
f(V) = V³ − 80.3V + 231 = 0
This equation is not easily factorable by hand, so we proceed with numerical methods or graphing techniques to find the roots.
🔹 Step 3: Solve Using a Graphing Calculator or Solver
By inputting f(V) = V³ − 80.3V + 231 into a graphing calculator or numerical root-finder (such as Newton-Raphson method), we can find the approximate roots:
- V₁ ≈ 3.34
- V₂ ≈ 6.81
- V₃ ≈ −10.15
Depending on the context, only the positive roots might be relevant to the physical or mathematical problem being solved.
✅ Final Answer:
The values of V that satisfy the equation V³ = 80.3V − 231 are approximately:
V = 3.34 and V = 6.81 (positive real roots)