MATH SOLVE

3 months ago

Q:
# Use the Newton-Raphson method to determine the solution of the simultaneous nonlinear equations: y=βx2+x+0.75 y+5xy=x2 Use the initial guesses of x = y = 1.2, and iterate until the 4th iteration. (Round the final answers to five decimal places.) The values of x and y are as follows: iterationxy01.21.21 0.0290321.39412 3 0.239294

Accepted Solution

A:

Answer:Step-by-step explanation:Let's solve for y.
βx2+x+0.75y+5xy=x2
Step 1: Add x^2 to both sides.
βx2+5xy+x+0.75y+x2=x2+x2
5xy+x+0.75y=2x2
Step 2: Add -x to both sides.
5xy+x+0.75y+βx=2x2+βx
5xy+0.75y=2x2βx
Step 3: Factor out variable y.
y(5x+0.75)=2x2βx
Step 4: Divide both sides by 5x+0.75.
y(5x+0.75)
5x+0.75
=
2x2βx
5x+0.75
y=
2x2βx
5x+0.75
Answer:
y=
2x2βx
5x+0.75