CAT 2020 Linear and Quadratic Equations Question (Hard)

Question

How many distinct positive integer-valued solutions exist to the equation ?

Accepted Answer

Step 1 We are given the equation Let s define two expressions Let Let So, Step 2 Since A and B are integers and their product is 1, the only integer possibilities are or We will solve each case. --- Case 1 and Solve Solve Check if these values satisfy - For Not valid - For Not valid So, no solution

CAT 2020

Quantitative

Linear and Quadratic Equations

Hard

How many distinct positive integer-valued solutions exist to the equation $(x^2 - 7x + 11)^{(x^2 - 13x + 42)} = 1$ ?

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