Derive the intimation scheme for the system f1 x1 x2 x1 xy

Derive the intimation scheme for the system f_1 (x_1, x_2) = (x_1 - xy)2 + x_2 - 6 = 0. f_2 (x_2, x_2) - x_1 + (x_2 - 4)^2 - 12 = 0

Solution

Solution:                     sir your question image is verry blurred please again not seeing like this

first eq. is f₁(x₁,x₂)=(x₁-3)^2+x₂² -6=0 ...........1) & f₂(x₁,x₂)=x₁² +(x₂-4)^2-12............2)

from first eq. (x₁-3)^2+x₂² -6=0

x₂ =(6-(x₁-3)^2)^1/2=f₁(x₁)

when f₁(x₁) =0 then x₁=3+6^1/2 or3-6^1/2

from second eq.    f₂(x₁,x₂)=x₁² +(x₂-4)^2-12 =0

x₁=(12-(x₂-4)^2)^1/2=f₂(x₂)

when f₂(x₂) =0 then x₂=4+2(3)^1/2 or 4-2(3)^1/2

the vlue of x1 & x2 putting in eq. 1) & 2)

we get the value of function

the no. of value of x1 & x2 is 4 therefore four value of f1 and four value of f2     

x1=3+6^1/2 & x2=4+2(3)^1/2     then f1(x1,x2)=54.74 & f2(x1,x2)=29.59

x1=3+6^1/2 & x2=4-2(3)^1/2     then f1(x1,x2)=.37 & f2(x1,x2)=29.59

x1=3-6^1/2 & x2=4+2(3)^1/2      then f1(x1,x2)=54.74 & f2(x1,x2)=.313

x1=3-6^1/2 & x2=4-2(3)^1/2       then f1(x1,x2)=.37 & f2(x1,x2)=.3131