Question

Write the word or phrase that best completes each statement or answers the question.

Use Newton's method to find the positive fourth root of 3 by solving the equation
x4 - 3 = 0. Start with x1 = 1 and find x2.

please show me how to solve because its a short answer question. please don't make it confusing so i can rewrite. i cant afford to get this questions wrong

Answer 1

its x^4-3=0

Answer 2

\(f(1)=1-3=-2\) and \(f'(x)=4x^3\) so \(f'(1)=4\)
your first guess is \(1\)
your next guess is
\[1-\frac{f(1)}{f'(1)}=1-\frac{-2}{4}=\frac{3}{2}\]

Answer 3

so what does that mean?

Answer 4

do i write all of that? and then the next step would be to solve an equation using 3/2?

Answer 5

your first guess is \(x_1\) and your next guess is
\[x_2=x_1-\frac{f(x_1)}{f'(x_1)}\]

Answer 6

you were only asked for the next approximation, which in this case was \(\frac{3}{2}\)

Answer 7

so that equation that equals 3/2 is the answer?

Answer 8

so if i were to write this on a test everything you wrote at first would be correct? are u sure?

Answer 9

so where does the fourth root of 3 come in?

Answer 10

pretty sure, since you are only asked for the next approximation
the one after that would be
\[x_3=\frac{3}{2}-\frac{f(\frac{3}{2})}{f'(\frac{3}{2})}\] whatever that is

Answer 11

keep going and you will get closer and closer

Answer 12

so that is not the answer?

Answer 13

the first answer i wrote is a complete answer to the question asked

Answer 14

so why did u say keep going