GATE 2021 ME (ME2) – Question 45
Find the positive real root of $x^3-x-3=0$ using Newton-Raphson method. If the starting guess ($x_0$) is 2, the numerical value of the root after two iterations ($x_2$) is _____ (round off to two decimal places).
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Correct answer: 1.66 to 1.68
Explanation
The iteration is $x_{n+1}=x_n-(x_n^3-x_n-3)/(3x_n^2-1)$. First x₁=2−3/11=1.7272727.
Apply the same expression once more to get x₂=1.67369117. **Answer: 1.67**. The requested result is the second iterate, not the fully converged root.