CAT 2024 Linear and Quadratic Equations Question (Medium)

Question

If and are real numbers such that , then the value of is

Accepted Answer

Step 1 Divide the entire equation by 4 to simplify x 2 y 2 - xy - 2 y 4 0 --- Step 2 Try substitution. Let S 4x 5y Rightarrow S 2 4x 5y 2 So S 2 16x 2 40xy 25y 2 We aim to convert the original equation to match these terms. From the simplified form x 2 y 2 - xy - 2 y 4 0 Rightarrow x 2 - xy y 2 2 y

CAT 2024

Quantitative

Linear and Quadratic Equations

Medium

If $x$ and $y$ are real numbers such that $4x^2 + 4y^2 - 4xy - 6y + 3 = 0$ , then the value of $(4x + 5y)$ is

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