Xavier Aptitude Test 2017 Paper

Question : 48 of 97

Marks: +1, -0

If x and y are real numbers, the least possible value of the expression

4(x-2)^{2}+4(y-3)^{2}-2(x-3)^{2}

is:

Solution:

(b)

4(x-2)^{2}+4(y-3)^{2}-2(x-3)^{2}

⇒ 4\ (x^{2}+4-4 x\ )+4(y-3)^{2}-2\ (x^{2}-6 x+9 )

\⇒ 4 x^{2}+16-16 x+4(y-3)^{2}-2 x^{2}+12 x-18

⇒ 2 x^{2}-4 x-2+4(y-3)^{2}

\⇒ 2\ (x^{2}-2 x )+4(y-3)^{2}-2

\⇒ 2\l (x^{2}-2 x+1\ )+4(y-3)^{2}-4

\⇒ 2(x-1)^{2}+4(y-3)^{2}-4

This is minimum when

x=1 \& y=3 .

Hence min value is

-4

Go to Question:

Prev Question

Next Question