Question

17x² - 9xy + 8y² simplify​

Answer 1

Answer:

g(x) = √( x² + y² )

But we need to find the minimun of x² + y² => f(x) = x² + y²

g(x) = 17x² + 12xy + 8y² - 100 = 0

F(x) = f - λg = x² + y² - λ( 17x² + 12xy + 8y² - 100 )

Fx = 2x - 34xλ - 12yλ

Fy = 2y - 12xλ - 16yλ

Fλ = -( 17x² + 2xy + 8y² - 100 )

Fx = Fy = Fλ = 0

{ 2x - 34xλ - 12yλ= 0

{ 2y - 12xλ - 16yλ = 0

{ 17x² + 2xy + 8y² - 100= 0

{ x - 17xλ - 6yλ = 0

{ y - 6xλ - 8yλ = 0

{ 17x² + 2xy + 8y² - 100= 0

{ λ( 17x + 6y ) = x

{ y = λ(6x+8y)

{ 17x² + 2xy + 8y² - 100= 0

{ λ = x / ( 17x + 6y )

{ λ = y / (6x+8y)

{ 17x² + 2xy + 8y² - 100= 0

{ x / ( 17x + 6y ) = y / ( 6x + 8y )

{17x² + 2xy + 8y² - 100= 0

{ x( 6x + 8y ) = y( 17x + 6y )

{ 17x² + 2xy + 8y² - 100= 0

{ 6x² + 8xy = 17xy + 6y²

{ 17x² + 2xy + 8y² - 100= 0

{ 6x² - 6y² = 9xy

{ 17x² + 2xy + 8y² - 100= 0

{ 2x² - 2y² = 3xy

{ 17x² + 2xy -8y2-100=0

Answer 2

Answer:

$\huge \fcolorbox{black}{cyan}{♛answer♛} \\ = {17x}^{2} - 9xy - {8y}^{2} \\ {17x}^{2} - 17xy + 8xy - {8y}^{2} \\ = 17x(x - y) + 8y(x - y) \\ = (x - y)(17x + 8y)$