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Home Q & A Board Science-Related Homework Help Mathematics
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smlyslvmel@aol. smlyslvmel@aol.
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11 years ago
Show that the equation x^3 -5x +7 can be rearranged as x = cuberoot(ax+b) where a and b are constants whose values are to be stated. Use the associated iterative formula, starting with x = -2.7 to state a root of x^3-5x+7=0 correct to 2 decimal places. Show using the sign-change method that this is indeed to the required accuracy.
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wrote...
#1
11 years ago
x^3 -5x +7 can be rearranged
  as x = cuberoot(ax+b)
wrote...
#2
11 years ago
Your first "equation" is an exprssion, so I assume you mean

x^3 -5x +7= 0

If so, then just add (5x - 7) to both sides to get x^3 by itself:

x^3 = 5x - 7

And then take the cube root of both sides.  My calculation converges to -2.74734654030721 after 22 iterations, but is equal to -2.75, to two decimal places, from the second iteration on.  I can't help you with the "sign change method".  I don't see any change in sign in the differences from term to term, and the terms are all negative, so I can't see what is changing sign.
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