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Numerade Educator



Problem 18 Medium Difficulty

Use Newton's method to find all solutions of the equation correct to six decimal places.

$ \sqrt{x + 1} = x^2 - x $


$x \approx-0.484028,1.897179$


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Video Transcript

given this equation, the first thing we can do is find the directive of promise. Axe is two acts Maya Swan minus one over two times the square of X plus one. Now we know he could make the initial approximation access and gives your 0.52 So se r ex one is negative 0.5. That means our ax to fall in the equation list in the textbook. If you do X three and ex Royal find the overall. The X is negative zero point for a 40 to eight. Now, for the second estimate, as we said, x one would be, too. Which means Axe Chu is gonna be to minus off to divide by us from two, which is 1.9011 dot, dot dot And then if we do x three, we end up with very close 1.897 x for 1.97 and then same thing for x five, which means overall we conserve. X is 1.897 17942 Solutions on night of 0.48028 and positive 1.897179