Use Lagrange Multipliers to Find the Minimum Value of the Function

question 128

Short Answer

Use Lagrange multipliers to find the minimum value of the function subject to the given constraints.
$$f ( x , y , z , t ) = 7 x + 7 y + 7 z + 7 t , \quad 7 \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + t ^ { 2 } \right) = 8$$

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