CAT 2023 Linear and Quadratic Equations Question (Hard)

Question

If and are real numbers such that , then value of ?

Accepted Answer

Step 1 We are given Let us simplify the left-hand side First expand So the full left-hand side becomes Step 2 Now simplify the right-hand side Equating both sides Step 3 Bring all terms to one side Combine like terms Step 4 This is a quadratic in and . Let s try substituting to simplify. Let Then Su

CAT 2023

Quantitative

Linear and Quadratic Equations

Hard

If $x$ and $y$ are real numbers such that $x^2 + (x - 2y - 1)^2 = -4y(x + y)$ , then value of $x - 2y$ ?

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