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. $\pm \frac{5}{2}$
• D. $\pm \frac{7}{2}$

Answer 1

The correct option is B $\pm \frac{3}{2}$

GIven, $x+y=\frac{7}{2}$ and $xy=\frac{5}{2}$
$x+y=\frac{7}{2}$
Squaring both sides, we get
$=>(x+y{)}^2=(\frac{7}{2}{)}^2$
$=>x^2+y^2+2xy=\frac{49}{4}$
$=>x^2+y^2+2\times \frac{5}{2}=\frac{49}{4}$
$=>x^2+y^2+5=\frac{49}{4}$
$=>x^2+y^2=\frac{49}{4}-5$
$=>x^2+y^2=\frac{49-20}{4}$
$=>x^2+y^2=\frac{29}{4}$
Now,
$(x-y{)}^2=x^2+y^2-2xy$
$=\frac{29}{4}-2\frac{5}{2}$
$=\frac{29-20}{4}$
$=\frac{9}{4}$
$=>(x-y)=\sqrt{\frac{9}{4}}$
$=>(x-y)=\pm \frac{3}{2}$