x *y = 2
x+y=7 y = 7-x sub this into the first equation
x*(7-x) = 2
7x - x^2 -2 = 0
x^2-7x+2 = 0 Qudratic formula a = 1 b = -7 c = 2 { 7+- sqrt ( 49-8)} /2 x = 3.5 +- sqrt(10.25)= 6.702 and .2984
Let a and b be those 2 numbers.
\(\begin{cases}a+b=7\\ab=2\end{cases}\\ a + \dfrac{2}{a} = 7\\ a^2 -7a + 2 = 0\\ a = \dfrac{7 \pm \sqrt{45}}{2}\\ a = \dfrac{7 +3\sqrt5}{2} \text{ OR }a = \dfrac{7-3\sqrt5}{2}\\ \text{When }a = \dfrac{7+3\sqrt5}{2},b=\dfrac{7-3\sqrt5}{2}\\ \text{When }a = \dfrac{7-3\sqrt5}{2},b=\dfrac{7+3\sqrt5}{2}\\ \text{The solutions are }(a,b) = \left(\dfrac{7-3\sqrt5}{2},\dfrac{7+3\sqrt5}{2}\right)\text{ or }(a,b) = \left(\dfrac{7+3\sqrt5}{2},\dfrac{7-3\sqrt5}{2}\right)\)