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=[tex] \frac{- \sqrt{71}- \sqrt{47} }{2} [/tex] and [tex] \frac{- \sqrt{71}+ \sqrt{47} }{2} [/tex]
sub those for x
x=y+√71
note: √71=(2√71)/2
x=[tex] \frac{- \sqrt{71}- \sqrt{47} +2\sqrt{71}}{2} [/tex] ,[tex] \frac{\sqrt{71}- \sqrt{47}}{2} [/tex]
or
x=[tex] \frac{- \sqrt{71}+ \sqrt{47} +2\sqrt{71}}{2} [/tex] ,[tex] \frac{\sqrt{71}+ \sqrt{47}}{2} [/tex]
xy=[tex] \frac{\sqrt{71}- \sqrt{47}}{2} [/tex] times [tex] \frac{-\sqrt{71}- \sqrt{47}}{2} [/tex] or [tex] \frac{\sqrt{71}+ \sqrt{47}}{2} [/tex] times [tex] \frac{-\sqrt{71}+ \sqrt{47}}{2} [/tex]
the result is -6 both times
xy=-6
