CAT 2020 Inequalities Question (Hard)

Question

Given two positive numbers and such that their product . Find the minimum possible value of .

Accepted Answer

Step 1 We are given xy 2601 We need to minimize x 1 y 1 Step 2 First expand x 1 y 1 xy x y 1 Given , so x 1 y 1 2601 x y 1 2602 x y Thus, minimizing is equivalent to minimizing . Step 3 Since and are positive and , by AM-GM inequality x y geq 2 2 2 times 51 102 Equality occurs when . Step 4 Now x 1

CAT 2020

Quantitative

Inequalities

Hard

Given two positive numbers $x$ and $y$ such that their product $xy=2601$ . Find the minimum possible value of $(x+1)(y+1)$ .

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