Answer to Question #260845 in English for Zee

Question

given: x₁²+2x₂-2=0

x₁+4x₂²-4=0

Let (x₁⁰;x₂⁰)=(1;2) be an initial guess to (x₁;x₂). Compute the first approximation (x₁⁽¹⁾;x₂⁽¹⁾) using the Newton method.

Answer 1

^x1²+2x2=2

^x1+4x²=4

^{let x⁰1,=1 and x⁰2=2}

^=-2(2)+2=-2

^{hence first appropriation x¹1=-1 and x¹2= 1}