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=[tex] \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
x=[tex] \frac{-(-28)+/- \sqrt{(-28)^2-4(1)(7)} }{2(1)} [/tex]
x=[tex] 14+/- 3\sqrt{21} [/tex]
sub for y
y=7/x
y=[tex] \frac{7}{14+/-3 \sqrt{21} } [/tex]
the reciprocals are
[tex] \frac{14+/-3 \sqrt{21} }{7} [/tex] and [tex] \frac{1}{14+/-3 \sqrt{21} } [/tex]
times first one by [tex] \frac{14+/-3 \sqrt{21} }{14+/-3 \sqrt{21} } [/tex] and second by 7/7
[tex] \frac{(14+/-3 \sqrt{21} )(14+/-3 \sqrt{21} )+7}{(7)(14+/-3 \sqrt{21} )} [/tex]
evaluate the plus and minus yourself please, my head hurts
