Determine the Minimum Value of F(x, Y) = $x ^ { 2 }$

question 83

Short Answer

Determine the minimum value of f(x, y) = $x ^ { 2 }$ - xy + 2 $y ^ { 2 }$ + 4 subject to the constraint $x - y - 1 = 0$ Enter your answer exactly as just a, b where a is the minimum and b is the Lagrange multiplier, using integers or reduced fractions of form $\frac { \mathrm { c } } { \mathrm { d } }$ (no words or units).

---

Definitions:

Great Toe

The largest and innermost toe of the human foot, also commonly referred to as the big toe.

Latex Allergy

A hypersensitivity reaction to the proteins present in natural rubber latex, leading to various allergic symptoms upon exposure.

Preoperative Assessment

An evaluation process conducted before surgical procedures to determine a patient's readiness and to minimize risks.

Obesity

A medical condition characterized by excessive body fat accumulation that presents a risk to health.