Question

Using xn 1 = -3 -(5/x²) with x0 = -4.25 find the values of x1, x2 and x3 using iteration?

Answer 1

To find the values of x1, x2, and x3 using iteration for the given equation, substitute the given values into the equation. The values of x1, x2, and x3 are -3.2776, -3.4649, and -3.4140 respectively.

Step-by-step explanation:

To find the values of x1, x2, and x3 using iteration for the equation xn+1 = -3 - (5/x²) with x0 = -4.25, we can substitute the given values into the equation.

1. For x1, we substitute x0 = -4.25 into the equation: x1 = -3 - (5/(-4.25)²) = -3 - (5/18.0625) = -3 - 0.2776 = -3.2776.
2. For x2, we substitute x1 = -3.2776 into the equation: x2 = -3 - (5/(-3.2776)²) = -3 - (5/10.7540) = -3 - 0.4649 = -3.4649.
3. For x3, we substitute x2 = -3.4649 into the equation: x3 = -3 - (5/(-3.4649)²) = -3 - (5/12.0424) = -3 - 0.4140 = -3.4140.