A problem of positive proportion function and inverse proportion function It is known that the positive scale function y = ± X and the inverse scale function y = K / X (K ≠ 0) intersect at points a and B. the positive scale function y = MX (m ≠ ± 1, m ≠ 0) intersects the inverse scale function y = K / X (K ≠ 0) at points c and D. is the length of line AB always less than the length of line CD? If not, please prove. If not, request the value range of K when the length of line AB is always less than the length of line CD

AB=2|k|
Y = the distance from any point on K / X to the origin
L=(x^2+y^2)^0.5
x^2+y^2≥2|xy|
When | x | = | y |, lmin = √ (2 | XY |)
|xy|=|k|
Lmin = | K | √ 2
|x|=|y|
y=±x
AB is the shortest

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