That looks plenty "nice" to me !pondzo said:Homework Statement
completing the squares; ## x^2+y^2+2xy-2x-2y+43 = 0##
The Attempt at a Solution
I did it as follows, but i would like to know if there is a different 'nicer' method to complete it;
## x^2 + y^2 + 2xy − 2x − 2y + 43 ##
## = (x + y)^2 − 2x − 2y + 43 ##
## = (x + y)^2 − 2(x + y) + 43 ##
## = (x + y)^2 − 2(x + y) + 1 + 42 ##
## = ((x + y) − 1)^2 + 42 ##
The purpose of completing the squares of a multivariable function is to rewrite the function in a simplified form that makes it easier to graph and analyze. It also helps to identify the minimum or maximum points of the function.
To complete the squares of a multivariable function, you need to group the terms with the same variables together, factor out the coefficient of the squared term, and then add and subtract a value to make the expression a perfect square.
Completing the squares of a multivariable function allows you to easily find the vertex or turning point of the function, which can give important information about the behavior of the function. It also helps to simplify the function and make it easier to solve for roots or zeros.
Completing the squares of a multivariable function is useful when working with quadratic functions or when trying to find the minimum or maximum points of a function. It can also be helpful in simplifying complex expressions and solving equations.
No, completing the squares of a multivariable function is only applicable to quadratic functions or functions that can be written in the form of ax^2 + bx + c, where a, b, and c are constants. It cannot be used for functions with higher degree terms or trigonometric functions.