1. Tardigrade
  2. Question
  3. Mathematics
  4. If x, y ∈ R then the minimum value of the expression E=x2+6 y2-2 x y+6 x-16 y+18 is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $x, y \in R$ then the minimum value of the expression $E=x^2+6 y^2-2 x y+6 x-16 y+18$ is

Complex Numbers and Quadratic Equations

Solution:

$ E=x^2+6 y^2-2 x y+6 x-16 y+18$
$ \Rightarrow\left(x^2+y^2-2 x y+6 x-6 y+9\right)+\left(5 y^2-10 y+5\right)+4 $
$ \Rightarrow(x-y+3)^2+5(y-1)^2+4$
Min. value for $y =1 ; x =-2 ; \min$. value is 4 .