solve the equations
first one
take the sqrt of both sides
x-y=√71
add y to both sides
x=y+√71
sub y+√71 for x in other part
(y+√71)²+y²=59
y²+2y√71+71+y²=59
2y²+2y√71+71=59
minus 59 both sides
2y²+2y√71+12=0
factor out 2
2(y²+y√71+6)=0
use quadratic equation or something
y=\(\frac{- \sqrt{71}- \sqrt{47} }{2}\) and \(\frac{- \sqrt{71}+ \sqrt{47} }{2}\)
sub those for x
x=y+√71
note: √71=(2√71)/2
x=\(\frac{- \sqrt{71}- \sqrt{47} +2\sqrt{71}}{2}\) ,\(\frac{\sqrt{71}- \sqrt{47}}{2}\)
or
x=\(\frac{- \sqrt{71}+ \sqrt{47} +2\sqrt{71}}{2}\) ,\(\frac{\sqrt{71}+ \sqrt{47}}{2}\)
xy=\(\frac{\sqrt{71}- \sqrt{47}}{2}\) times \(\frac{-\sqrt{71}- \sqrt{47}}{2}\) or \(\frac{\sqrt{71}+ \sqrt{47}}{2}\) times \(\frac{-\sqrt{71}+ \sqrt{47}}{2}\)
the result is -6 both times
xy=-6
