Question

if x-y=8 and xy=9 then find x+y​

Answer 1

$\huge\bold{\color{aqua}{Solution :-}}$

$\bold{\purple{\text{ it's given in the question }}}$

$\qquad\bold{\color{blue}{x-y=\color{lime}{8}\quad \color{green}{;} \quad\color{blue}{ xy=}\color{lime}{\:9}}}$

$\bold{\purple{\text{To find the value of }}}$

$\qquad\bold{\color{red}{x+y }}$

$\purple{\bold{\text{We know that}}}$

$\quad\orange{\bold{(x+y)^2=(x-y)^2+4xy}}$

$\purple{\bold{\text{On substituting values }}}$

$\Rightarrow\bold{(x+y)^2=(8)^2+4(9)}$

$\Rightarrow\bold{(x+y)^2=64+36}$

$\Rightarrow\bold{(x+y)^2=100}$

$\Rightarrow\bold{x+y=\pm\sqrt{100}}$

$\Rightarrow\bold{\green{\boxed{\red{x+y}=\pink{\pm 10}}}}$