Question : If $x + y = 10$, $2xy = 48$ and $x > y$, then find $2x - y$.
Option 1: 6
Option 2: 8
Option 3: 4
Option 4: 3
Correct Answer: 8
Solution :
Given that $x + y = 10$ and $2xy = 48$,
$⇒y = 10 - x$
Substituting this into the second equation,
$⇒2x(10 - x) = 48$
$⇒x^2-10x+24=0$
$⇒(x-4)(x-6)=0$
$x = 6$ and $x = 4$
But given that $x > y$, we take $x = 6$.
Substituting $x = 6$ into the equation $y = 10 - x$,
$⇒y = 4$
Finally, substituting $x = 6$ and $y = 4$ into the expression $2x - y$ gives:
$⇒2x - y = 2(6) - 4 = 8$
Hence, the correct answer is 8.
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