Question

Find the positive root of x^3-x=1 correct to four decimal places by bisection method​

Answer 1

Given :   x³  - x  =  1  

To Find :  positive root   correct to four decimal places by bisection method​

Solution:

x³  - x  =  1  

=> x³  - x  -  1 = 0  

f(x)  = x³  - x  -  1

x = 0 => f(x) = - 1

x = 1  => f(1)  = 1 - 1 - 1 =  -1

x = 2 =>   f(2) = 8 - 2 - 1 = 5

f(1) is -ve  and f(2) is +ve

Hence root lies between  1 and 2

(1 + 2) /2  = 1.5  

f(1.5)  = 0.875  is +ve

Hence lies between  1 and  1.5  and so on

x   f(x)

1 -1

2 5

1.5 0.875

1.25 -0.296875

1.375 0.224609375

1.3125 -0.051513672

1.34375 0.082611084

1.328125 0.014575958

1.3203125 -0.018710613

1.32421875 -0.002127945

1.326171875 0.00620883

1.325195313 0.002036651

1.324707031 -4.65949E-05

1.324951172 0.000994791

1.324829102 0.000474039

1.324768066 0.000213707

1.324737549 8.35524E-05

1.32472229 1.84779E-05

1.324714661 -1.40587E-05

1.324718475 2.20949E-06

1.3247  is correct value upto 4 decimal place

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