GATE 2022 CE (CE1) – Question 29
For initial guess $x_1=1$, use $x_{n+1}=\frac12(x_n+P/x_n)$. For P=2 and P=3, x₅ rounds to 1.414 and 1.732. If P=10, what is x₅ (three decimals)?
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Correct answer: 3.146 to 3.178
Explanation
Start with $x_1=1$ and use P=10. The successive iterates are $x_2=5.5$, $x_3=3.6590909$, $x_4=3.1960051$, and $x_5=3.1624556$.
Thus the specified fifth iterate rounds to **3.162**. Count four updates from x₁ to x₅; the exact limit is $\sqrt{10}$.