Question

If $x+y=\frac{7}{2}$ and $xy=\frac{5}{2}$. Find the value of: $\left(i\right)(x-y)$ $\left(ii\right)(x^2-y^2)$

Answer 1

$x+y=7/2$ $xy=5/2$

$(x-y{)}^2=(x+y{)}^2-4xy$

$={\left(\frac{7}{2}\right)}^2-4\left(\frac{5}{2}\right)$

$=\frac{49}{4}-\frac{20}{2}$

$=\frac{49-40}{4}=\frac{9}{4}$

$x-y=\pm \sqrt{\frac{9}{4}}=\pm \frac{3}{2}$

$(x^2-y^2)=(x+y)(x-y)$

$=\left(\frac{7}{2}\right)(\pm \frac{3}{2})$

$=\pm \frac{21}{4}$