f(x,y)= (x-2)2 + 2(y-2)2 - 100 g(x,y) = -34+x2+24x-9y

(x0,y0 = (4,9) is an initial estimate of the solution of f(x, y) = 0 and g(x,y) = 0, then using Newton's method find the next approximate solution. 

Do all calculations to at least eight decimal digit accuracy. Your answers can be rounded to five decimal digit accuracy when entered. Or they can be entered as an exact rational expression


X1 and Y1

in Other Math Topics by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Here’s one way to apply Newton’s Method.



Substitute for y in f(x,y)=0:









More to follow...

by Top Rated User (787k points)

Continued from above solution:

After substitution: x₁=4.071964018, y₁=(x₁²+24x₁-34)/9=8.923114155.

Rounding: (4.07196,8.92311).

A more accurate solution after a couple more iterations:

x₃=4.070487838, y₃=(x₃²+24x₃-34)/9=8.91784215.

Rounding to 5 decimal places (4.07049,8.91784).

Note that there is another intersection point (see graph).

Related questions

0 answers
0 answers
1 answer
1 answer
1 answer
asked Nov 17, 2013 in Other Math Topics by Ziggy1423 Level 1 User (120 points) | 213 views
1 answer
asked Sep 1, 2013 in Other Math Topics by jeffreycliffor Level 1 User (120 points) | 141 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
85,407 questions
90,921 answers
103,272 users