Final answer:
The minimum possible value of the sum of squares of the two other numbers is 40, obtained by applying the arithmetic mean-geometric mean inequality under the constraint xy = 20, which originates from the multiplication by the incorrect number leading to an increase in the product by 720. None of the options are correct.
Step-by-step explanation:
Let the two real numbers Ashok was supposed to multiply by 37 be x and y. Instead, Ashok multiplied them by 73, resulting in a product that was 720 more than expected. So we can set up the equation: (73x - 37x)y = 720, which simplifies to 36xy = 720. Dividing both sides by 36 gives xy = 20.
To find the minimum possible value of the sum of squares of the other two numbers, we want to minimize x2 + y2 under the constraint xy = 20. Using the arithmetic mean-geometric mean inequality, we have (x2 + y2)/2 ≥ √(x2y2), which simplifies to x2 + y2 ≥ 2√(202) = 40. Since x2 and y2 are both positive, the minimum sum of squares occurs when x = y = √20. Thus, the minimum possible value of their sum of squares is 2(√20)2 = 2(20) = 40.