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Maths-

General

Easy

Question

If $x minus 2 y equals 4$ , the minimum value of $x y$ is

-2
0
0
-3

The correct answer is: -2

Given, $x minus 2 y equals 4$
Let $A equals x y blank rightwards double arrow blank A equals 2 y to the power of 2 end exponent plus 4 y$

$rightwards double arrow blank fraction numerator d A over denominator d y end fraction equals 4 plus 4 y$

For extremum value, $fraction numerator d A over denominator d y end fraction equals 0$

$rightwards double arrow blank y equals negative 1$

Now, $fraction numerator d to the power of 2 end exponent A over denominator d y to the power of 2 end exponent end fraction equals 4 greater than 0$ , minima

At $y equals negative 1$ ,

$x equals 4 plus 2 open parentheses negative 1 close parentheses equals 2$

$therefore blank A equals x y equals 2 open parentheses negative 1 close parentheses equals negative 2$

$therefore$ Minimum value of $x y$ is $negative 2$

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