Question #200888

Find the real roots of the equation x^3 + x^2 - 100= 0 by the iteration method


1
Expert's answer
2021-05-31T17:32:28-0400

43+42100<04^3+4^2-100<0

53+52100>05^3+5^2-100>0

So, the root is between 4 and 5.


x2(x+1)=100x^2(x+1)=100

x=10x+1x=\frac{10}{\sqrt{x+1}}

Let the initial approximation be x0=4.5x_0=4.5

x1=10/4.5+1=4.26x_1=10/\sqrt{4.5+1}=4.26

x2=10/4.26+1=4.35x_2=10/\sqrt{4.26+1}=4.35

x3=10/4.35+1=4.32x_3=10/\sqrt{4.35+1}=4.32

x4=10/4.32+1=4.33558x_4=10/\sqrt{4.32+1}=4.33558

x5=10/4.33558+1=4.32921x_5=10/\sqrt{4.33558+1}=4.32921

x6=10/4.32921+1=4.33180x_6=10/\sqrt{4.32921+1}=4.33180

x7=10/4.33180+1=4.33117x_7=10/\sqrt{4.33180+1}=4.33117

Since the difference between x6 and x7 are very small, so the root is 4.33117


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Comments

Assignment Expert
01.07.21, 00:58

Dear George, please use the panel for submitting a new question.


George
30.05.21, 18:39

Find the negative root of the equation x^3 - 2x + 5 =0

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