SOLUTION: Among all pairs of numbers (x,y) such that 4x+2y=22, find the pair for which the sum of squares, x2+y2, is minimum. Write your answers as fractions reduced to lowest terms.
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Question 1166569: Among all pairs of numbers (x,y) such that 4x+2y=22, find the pair for which the sum of squares, x2+y2, is minimum. Write your answers as fractions reduced to lowest terms. Answer by ikleyn(52834) (Show Source):
Express y = = 11 - 2x from the linear equation and then substitute it into the quadratic form.
By doing this way, you will get the quadratic form in one unknown
x^2 + y^2 = x^2 + (11-2x)^2 = x^2 + 121 - 44x + 4x^2 = 5x^2 - 44x + 121.
Then you can use EITHER Calculus OR the formula for the vertex
x = " - " = = = 4.4.
