x+y=28
xy=7
xy=7
divide both sides by x
y=7/x
sub 7/x for y in first equation
7/x+x=28
times both sides by x
7+x^2=28x
minus 28x from both sides
x^2-28x+7=0
use quadratic formula
if
ax^2+bx+c=0
x=\(\frac{-b+/- \sqrt{b^2-4ac} }{2a}\)
x=\(\frac{-(-28)+/- \sqrt{(-28)^2-4(1)(7)} }{2(1)}\)
x=\(14+/- 3\sqrt{21}\)
sub for y
y=7/x
y=\(\frac{7}{14+/-3 \sqrt{21} }\)
the reciprocals are
\(\frac{14+/-3 \sqrt{21} }{7}\) and \(\frac{1}{14+/-3 \sqrt{21} }\)
times first one by \(\frac{14+/-3 \sqrt{21} }{14+/-3 \sqrt{21} }\) and second by 7/7
\(\frac{(14+/-3 \sqrt{21} )(14+/-3 \sqrt{21} )+7}{(7)(14+/-3 \sqrt{21} )}\)
evaluate the plus and minus yourself please, my head hurts
