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Find iteration method 2x^3-2x-5, a=1, b=4

Solution:
Your problem `->` iteration method 2x^3-2x-5, a=1, b=4


Method-1
Let `f(x)=2x^3-2x-5`

`2x^3-2x-5=0`

`:.2x^3-2x=5`

`:.2x(x^2-1)=5`

`:.2x=(5)/(x^2-1)`

`:.x=((5)/(x^2-1))/2`

`:.phi(x)=((5)/(x^2-1))/2`


Here `f(1) = -5 < 0` and `f(4) = 115 > 0`

`:.` Root lies between `1` and `4`

`x_0 = (1 + 4)/2 = 2.5`


`x_1 = phi(x_0) = phi(2.5) = 0.4762`

`x_2 = phi(x_1) = phi(0.4762) = -3.2331`

`x_3 = phi(x_2) = phi(-3.2331) = 0.2645`






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