Find x and y such that subject to the condition attains a minimum value.
B)
C)
D)

Question

Find x and y such that  subject to the condition  attains a minimum value. ​
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

To find the values of x and y that minimize the given expression, we need to solve for the roots of the equation:

11eb0d3b_98bc_97e1_9790_655b61572ad5_TB1243_11 = (x + y + 1)^2 + (x - y - 1)^2

Expanding the equation, we get:

11eb0d3b_98bc_97e1_9790_655b61572ad5_TB1243_11 = 2(x^2 + y^2 + 1) + 2

Simplifying further, we get:

(x^2 + y^2) = (1/2) * (11eb0d3b_98bc_97e1_9790_655b61572ad5_TB1243_11 - 2)

Since we want to minimize the expression, we want to find the smallest value of (x^2 + y^2) that satisfies this equation. The smallest value of the right-hand side is achieved when 11eb0d3b_98bc_97e1_9790_655b61572ad5_TB1243_11 is minimized, which occurs when x = 0 and y = 0. Substituting these values, we get:

(x^2 + y^2) = 0.5 * (11eb0d3b_98bc_97e1_9790_655b61572ad5_TB1243_11 - 2) = 0.5 * 11eb0d3b_98bc_97e0_9790_330a0c6e9027_TB1243_11

Thus, the minimum value is achieved when x = 0 and y = 0, and the answer is choice C, 11eb0d3b_98bc_97e4_9790_49e29a8a1396_TB1243_11.

Find X and Y Such That Subject to the Condition