Question

please answer this question fast. it's from algebraic identities
${x}^{2} + {y}^{2} = 77$
and
$xy = 14$
what are the possible values of x-y ? ​

Answer 1

$\text\color{fuchsia}{Given -}$

$\color{aqua}{{x}^{2}+{y}^{2}} = 77 ,$ $\color{aqua}{xy = 14}$

$\text\color{fuchsia}{Identity to be used - }$

$\color{aqua}{{(x-y)}^{2} = {x}^{2}+{y}^{2} - 2xy}$

$\text\color{fuchsia}{Solution - }$

$\color{aqua}{\hookrightarrow{(x-y)}^{2} = {x}^{2}+{y}^{2} - xy}$

$\color{aqua}{\hookrightarrow{(x-y)}^{2} = 77 - 2(14)}$

$\color{aqua}{\hookrightarrow{(x-y)}^{2} = 77 - 28}$

$\color{aqua}{\hookrightarrow{(x-y)}^{2} = 49}$

$\color{maroon}{\hookrightarrow x-y = 7 }$

$\color{orange}\fbox{Useful ?? ⇢ Brainlist}$