Question

In the secant method to estimate
the root of Equation x3-X-2= 0, if
x1=1 and x2=2 are initial
estimates then x3 =​

Answer 1

Estimates of x3 using second approximation is  x3 = 1.33333 (+ve)

Given:

The root of Equation is $x^{3}$ - x -2 = 0 and x1 = 1 , x2 = 2

To Find:

To estimate the value of x3 from the equation

Solution:

Since, x1 = 1 and x2 = 2

f(x1) = 1 - 1 - 2

 = -2 (-ve)

f(x2) = 8 - 2 - 2

= 4 (+ve)

By secant method,

Using second approximation,

x3 = $\frac{ x1f(x2) - x2 f(x1)}{f(x2) - f(x1)}$

= $\frac{(1)(4) - (2)(-2)}{4+2}$

x3 = 1.33333 (+ve)

Estimates of x3 using second approximation is  x3 = 1.33333 (+ve)

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