If x and y are real numbers and 4x^2+2xy+9y^2=100 then

Halle Marsh

Halle Marsh

Answered question

2022-04-22

If x and y are real numbers and 4x2+2xy+9y2=100 then what are all possible values of x2+2xy+3y2.

Answer & Explanation

botassaiby

botassaiby

Beginner2022-04-23Added 16 answers

Hint: The problem amounts to minimizing and maximizing x2+2xy+3y2 subject to the constraint 4x2+2xy+9y2=100. The possible values of x2+2xy+3y2 will be the closed interval from the minimum to the maximum.
Finding the necessary minimum and maximum can then be tackled using the method of Lagrange multipliers.

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