Algebra
Minimum of rational expression in two variables
MJMT_Full_Test_05
Grade 12
Question:
If the minimum value of $\dfrac{x^2y^2-2xy^2+2y^2+4xy-4y+4}{xy^2+2y}$ is '$k$' $\forall\,x,y\in\mathbb{R}^+$, then $[10k]$ equals (where $[\cdot]$ is GIF)
Step-by-Step Solution
Key Concept: Rewrite numerator as $(xy-y+2)^2+(xy+2-2y)^2$... or complete the square. Find minimum by AM-GM or substitution.
$[10k]=8$.
Correct Answer: 8