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Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of newton raphson’s method (up to two decimal places) is
  • a)
    0.233
  • b)
    0.686
  • c)
    0.889
  • d)
    0.614
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Starting with x = 1, the solution of the equation x3 + x = 1, after tw...
To solve the equation x^3 - x = 1 using Newton-Raphson method, we need to find the derivative of the function f(x) = x^3 - x - 1.

Taking the derivative, we get:
f'(x) = 3x^2 - 1

Now, let's apply the Newton-Raphson method for two iterations:

Iteration 1:
x1 = x0 - (f(x0) / f'(x0))

Substituting x0 = 1 into the equation:
x1 = 1 - ((1^3 - 1) / (3(1^2) - 1))
x1 = 1 - (1 / 2)
x1 = 1 - 0.5
x1 = 0.5

Iteration 2:
x2 = x1 - (f(x1) / f'(x1))

Substituting x1 = 0.5 into the equation:
x2 = 0.5 - ((0.5^3 - 0.5) / (3(0.5^2) - 1))
x2 = 0.5 - (0.125 - 0.5) / (3(0.25) - 1)
x2 = 0.5 - (-0.375) / (0.75 - 1)
x2 = 0.5 - (-0.375) / (-0.25)
x2 = 0.5 + 1.5
x2 = 2

After two iterations of Newton-Raphson method, the solution of the equation x^3 - x = 1 starting with x = 1 is x = 2.
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Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of newton raphson’s method (up to two decimal places) isa)0.233b)0.686c)0.889d)0.614Correct answer is option 'B'. Can you explain this answer?
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Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of newton raphson’s method (up to two decimal places) isa)0.233b)0.686c)0.889d)0.614Correct answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of newton raphson’s method (up to two decimal places) isa)0.233b)0.686c)0.889d)0.614Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of newton raphson’s method (up to two decimal places) isa)0.233b)0.686c)0.889d)0.614Correct answer is option 'B'. Can you explain this answer?.
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