CAT 2018 Slot 1 QA Question 33: While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other tw

Question

While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other tw

Accepted Answer

Let the product of the other two real numbers be p.
The increase in the product is
$73p - 37p = 720$
$36p = 720$
$p = 20$
Let the other two real numbers be a and b. Then $ab = 20$.
$a^{2} + b^{2} = (a - b)^{2} + 2ab$
$a^{2} + b^{2} = (a - b)^{2} + 40$
This is minimum when $a = b$, so the minimum val

While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is