If the value of $xy$ , If $ x^2 + y^2 = 34$ and $x + y =8$ If $ x^2 + y^2 = 34$ and $x + y =8$ find the value of xy
So what should I be considering here the sum of two squares or..
I'm struggling here & any help to figure this out will be kindly appreciated

$x^2$ + $y^2$ = $34$ $-->$ Equation 1
$x + y = 8$ $-->$ Equation 2
Now, we can rewrite Equation 2 with respect to x. This value will be substituted into Equation 1.
$x = 8 - y$
$x^2 + y^2 = 34$
$(8 - y)^2 + y^2 = 34$
$64 - 16y + y^2 + y^2 = 34$
$64 - 16y + 2y^2 = 34$
$2y^2 - 16y + 30 = 0$
Solving the quadratic above, the roots are: $$y1 = 5$$ and $$y2 = 3$$
Now plug both of these values into Equation 2. This will help you find the corresponding x-value. Once this is obtained, multiply the two numbers.
$x + y = 8$
$x + 5 = 8$
$x = 3$
$$xy = 3(5) = 15$$
This is the first solution.
$x + y = 8$
$x + 3 = 8$
$x = 5$
$$xy = 5(3) = 15$$
In both cases, the solution is 15, and this is due to the symmetry of the two points. Therefore, xy must be equal to 15.
