CAT 2024 Slot 2 QA Question 7: f $x$ and $y$ are real numbers such that $4x^2 + 4y^2 - 4xy - 6y + 3 = 0$, then the value of $(4x + 5y)$ is

Question

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

Accepted Answer

Complete the squares in the given expression.
$4x^2 + 4y^2 - 4xy - 6y + 3 = 0$
$\Rightarrow (2x-y)^2 + 3y^2 - 6y + 3 = 0$
$\Rightarrow (2x-y)^2 + 3(y-1)^2 = 0$
Since both terms are non-negative, each must be $0$.
$y = 1$
$2x - y = 0$
$\Rightarrow x = \dfrac{1}{2}$
$4x + 5y = 4 	imes \dfrac{1}{2} +

f xxx and yyy are real numbers such that 4x2+4y2−4xy−6y+3=04x^2 + 4y^2 - 4xy - 6y + 3 = 04x2+4y2−4xy−6y+3=0, then the value of (4x+5y)(4x + 5y)(4x+5y) is

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