CAT 2020 Linear and Quadratic Equations Question (Easy)

Question

In how many ways can a pair of integers be chosen such that x 2 - 2 x a - 2 0 , ?

Accepted Answer

Step 1 We are given the equation We analyze this by considering possible integer values of and checking when becomes an integer. Let , so Then the equation becomes a - 2 2y - y 2 a - 2 2y - y 2 0y 2 - y 0y 0, 1, 2 yxay 0 a - 2 0a 2 x 0x 0y 1 a - 2 1a 1a 3 x 1x 1y 2 a - 2 0a 2 x 2x 2 x, a 2,2 , 2,2 S

CAT 2020

Quantitative

Linear and Quadratic Equations

Easy

In how many ways can a pair of integers $(x, a)$ be chosen such that
$x^2 - 2|x| + |a - 2| = 0 \, ?$

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