x.y=30 and x+y=10.3 ,what is x & Y.

Question

final answer is x=5.15+1.86i
and y=5.15-186i, this way is by try and error (logic). but can somebody please show me how you do it by aljebra, please, thank you.

Answer 1

xy=30
x+y=10.3

30/y + y=10.3

30+y^2=10.3y

y^2-10.3y+30=0
quadratic equation.

y= (10.3 +-sqrt(10.3^2 -120))/2

solve that.

Answer 2

that is the problem i cant solve it because i will end up with square root of -13.91. please solve this equation for me.

Answer 3

Goodness. I will do the sqrt for you.

sqrt(10.3^2-120)=sqrt(-13.91)=
=sqrt(13.91)(sqrt-1)=sqrt(13.91)i
=3.72i

SO you have:
(10.3+-3.72i)/2=5.15+-1.86i

Answer 4

very good, but when i want to proove it by x + y =10.3,
x=30/(5.15+1.84i), y=(5.15+1.84i)
how you drive this equation
30/(5.15+1.84i)+(5.15+1.84i)=10.3
thank you