Question

What are numbers that when multiplied, is 6, and when added is 13?

Answer 1

xy=6
x+y=13

x+y=13
minus x
y=13-x
sub for y in other equation
x(13-x)=6
13x-x^2=6
add -13x+x^2 to both sides
0=x^2-13x+6
use quadratic formula
for
ax^2+bx+c=0
x=
`\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}`

a=1
b=-13
c=6

x=
`\frac{-(-13)+/- \sqrt{(-13)^(2)-4(1)(6)} }{2(1)}`
x=
`(13+/- √(169-24) )/(2)`
x=
`(13+/- √(145) )/(2)`
x=
`(13+ √(145) )/(2)` or
`(13- √(145) )/(2)`
aprox
x=12.5208 or0.479203

the numbers are 12.5208 and 0.479203