Question

If $x+y=\frac{7}{2}$ and $xy=\frac{5}{2}$; find $x-y$.

• A. $\pm \frac{1}{2}$
• B. $\pm \frac{3}{2}$
• C. $\pm \frac{3}{4}$
• D. $\pm \frac{13}{2}$

Answer 1

Answer: (B)

$\pm \frac{3}{2}$

Given,
$x+y=\frac{7}{2},xy=\frac{5}{2}$
we know, $(x+y{)}^2-(x-y{)}^2=4xy$
$=>(\frac{7}{2}{)}^2-(x-y{)}^2=4\times \frac{5}{2}$
$=>\left(\frac{49}{4}\right)-(x-y{)}^2=\frac{20}{2}$
$=>-(x-y{)}^2=\frac{20}{2}-\frac{49}{4}$
$=>-(x-y{)}^2=\frac{40-49}{4}$
$=>-(x-y{)}^2=-\frac{9}{4}$
$=>x-y=\sqrt{\frac{9}{4}}$
$=>x-y=\pm \frac{3}{2}$