Maths question from Laboratory Attendant exam, 2026 by JKSSB
If x and y are real numbers, then the minimum value of x ^ 2 + 4xy + 6y ^ 2 - 4y + 4 is
Last updated Jun 19, 2026
Correct Answer:
Option C —
2
We can find the lowest possible value of this expression by reorganizing it into perfect squares. In the world of real numbers, any number multiplied by itself (squared) can never be negative; the absolute smallest value a squared group can ever have is zero.
Grouping the parts:
We can break apart the original expression and group the pieces together so that they form two separate squared terms, with a plain number left over at the end.
The first squared group:
We take the first variable squared, the part where the two variables are multiplied together, and a portion of the second variable squared. These blend perfectly into one large squared package.
The second squared group:
With the pieces of the second variable that remain, we can form a second, smaller squared package.
Finding the lowest total:
Once everything is rewritten, the entire expression becomes: the first squared package, plus the second squared package, plus the number two.
To make the total as small as possible, we want both of those squared packages to be at their absolute minimum. Since neither can drop below zero, the lowest they can possibly go is zero. When both packages shrink all the way down to zero, we are left only with that final independent number at the end, which is two.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
