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实数

x, y

满足

x^{2}+2 x y-3 y^{2}=1

，则

x^{2}+y^{2}

的最小值是

Mar 8, 2024

实数

x, y

满足

x^{2}+2 x y-3 y^{2}=1

，则

x^{2}+y^{2}

的最小值是

Generated Graph

Solution by Steps

step 1

To find the minimum value of

x^2 + y^2

subject to the constraint

x^2 + 2xy - 3y^2 = 1

, we can use the method of Lagrange multipliers or directly find the critical points of the function

step 2

The asksia-ll calculator has computed the minimum value of

x^2 + y^2

given the constraint and found two points where this minimum occurs:

(-0.875392, -0.206652)

and

(0.875392, 0.206652)

step 3

The minimum value of

x^2 + y^2

subject to the given constraint is approximately

0.809017

Answer

The minimum value of

x^2 + y^2

subject to the constraint

x^2 + 2xy - 3y^2 = 1

is approximately

0.809017

Key Concept

Optimization with constraints

Explanation

The minimum value of a function subject to a constraint can be found using optimization techniques such as Lagrange multipliers, which is likely the method used by the asksia-ll calculator to find the approximate minimum value.