Examples of Math Problems: how to solve 10th root of 1.6

Thursday, April 3, 2014

how to solve 10th root of 1.6

From numerical methods we can write
f%28x%29=x%5E10-1.6

f%28x%29=x%5E10-1.6

and use Newton's method to get:

x%5Bn%2B1%5D=%289x%5Bn%5D%5E10%2B1.6%29%2F%2810x%5Bn%5D%5E9%29

x%5Bn%2B1%5D=%289x%5Bn%5D%5E10%2B1.6%29%2F%2810x%5Bn%5D%5E9%29

which converges very fast:
x%5B1%5D=1.00%29%29%29%0D%0A%7B%7B%7Bx%5B2%5D=1.06

x%5B1%5D=1.00%29%29%29%0D%0A%7B%7B%7Bx%5B2%5D=1.06

x%5B3%5D=1.0487037

x%5B4%5D=1.0481238

x%5B5%5D=1.0481223

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