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GATE 2025 Chemical Engineering, Q46 · Numerical Methods

The correct answer is 1.65 to 1.69.

Question

The Newton-Raphson method is used to find the root of f(x) ≡ x2−x² − x − 1 = 0. Starting with an initial guess x(0)=1,x_(0) = 1, the second iterate x(2)x_(2) is ____ (rounded off to 2 decimal places).

Official answer: 1.65 to 1.69

Why

GATE 2025 official key: 1.65 to 1.69.x(1)=1−1.69. x⁽¹⁾ = 1 − f(1)/f'(1) =1−(−1)/1=2.x(2)=2−= 1 − (−1)/1 = 2. x⁽²⁾ = 2 − f(2)/f'(2) =2−1/3≈1.667.= 2 − 1/3 \approx 1.667.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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