Word Count : 452

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समीकरण ( 2x^3 = 3x + 6 ) को न्यूटन-रैफसन विधि से हल करने के लिए पहले इसे शून्य के रूप में लिखते हैं: [ f(x) = 2x^3 - 3x - 6 ] और इसका अवकलज: [ f'(x) = 6x^2 - 3 ] न्यूटन-रैफसन पुनरावृत्ति सूत्र है: [ x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} ] प्रारंभिक अनुमान ( x_0 = 2 ) लेते हैं। पहली पुनरावृत्ति: [ f(2) = 2(2^3) - 3(2) - 6 = 16 - 6 - 6 = 4 ] [ f'(2) = 6(2^2) - 3 = 24 - 3 = 21 ] [ x_1 = 2 - \frac{4}{21} = 2 - 0.190476 \approx 1.8095 ] दूसरी पुनरावृत्ति: [ f(1.8095) = ____ _____ _____ ___ ______ __________ _______ _______ ________ _____ _________.
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