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:
Explanation:
4(x – 2)2 + 4(y – 3)2 – 2(x – 3)2
= 4(x2 + 4 – 4x) + 4(y – 3)2 – 2(x2 + 9 – 6x)
= 4(y – 3)2 + 2x2 – 4x – 2
Now, (y – 3)2 least value would be 0.
The least value of 2x2 – 4x – 2 would be at x = -(-4)/(2×2) = 1
The least value of 2x2 – 4x – 2 = 2(1)2 – 4(1) – 2 = -4
The least value of the expression would be = – 4.
Hence, option (b).
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