Find two numbers whose product is 12 and whose sum of squares is minimum?
A) (2, 6) and (-2, -6)
B) $- \sqrt { 12 } , - \sqrt { 12 } \text { and } \sqrt { 12 } , \sqrt { 12 }$
C) (3, 4) and (-3, -4)
D) $- \sqrt { 3 } , \sqrt { 4 } \text { and } \sqrt { 3 } , \sqrt { 4 }$

Question

Quizplus · Accepted Answer

The sum of squares is minimized when the two numbers are equal in magnitude, as shown by the equation $x^2 + y^2$ being minimized subject to the constraint $xy = 12$. This leads to $x = y = \sqrt{12}$ or $x = y = -\sqrt{12}$, which are the pairs given in option B.

Find Two Numbers Whose Product Is 12 and Whose Sum −12,−12 and 12,12- \sqrt { 12 } , - \sqrt { 12 } \text { and } \sqrt { 12 } , \sqrt { 12 }−12​,−12​ and 12​,12​

Find Two Numbers Whose Product Is 12 and Whose Sum $- \sqrt { 12 } , - \sqrt { 12 } \text { and } \sqrt { 12 } , \sqrt { 12 }$