Question 121

If x and y are real numbers, then the least possible value of $$4(x - 2)^2 + (y - 3)^2 - 2(x - 3)^2$$ is:

Solution

Expression : $$Z=4(x - 2)^2 + (y - 3)^2 - 2(x - 3)^2$$

Minimum value of a square term is 0, thus $$y=3$$

Now, if $$x>2$$ or $$x<0$$ then the term will be positive.

Case I : $$x=0$$ and $$y=3$$

=> $$Z=16+0-18=-2$$

Case II : $$x=1$$ and $$y=3$$

=> $$Z=4+0-8=-4$$

Case III : $$x=2$$ and $$y=3$$

=> $$Z=0+0-2=-2$$

$$\therefore$$ Minimum value of expression = -4

=> Ans - (B)

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