Question

What number multiplies to 12 but adds to 16

Answer 1

An answer would be 2
2+2+2+2+2+2=12
2*2*2*2=16

Another answer would be 4.
4+4+4=12
4*4=16

Answer 2

x+y=16

xy=12

x+y=16

subtract x from both side

y=16-x

subsitute for y

x(16-x)=12

16x-x^2=12

subtract add x^2 to both sides

16x=12+x^2

subtract 16x from both sides

x^2-16x+12=0

try and factor

can't

use quadratic equation which is

x=
`\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}` when you have
ax^2+bx+c=0
x^2-16x+12=0
a=1
b=-16
c=12
subsitute
x=
`\frac{-(-16)+/- \sqrt{(-16)^(2)-4(1)(12)} }{2(1)}`
x=
`(16+/- √(256-48) )/(2)`
x=
`(16+/- √(208) )/(2)`
x=
`(16+/- 4√(13) )/(2)`
x=
`8+/- 2√(13)`
x=
`8- 2√(13)` or
`8+ 2√(13)`
the answer is
the numbers are
`8- 2√(13)` and
`8+ 2√(13)` or
aprox 0.788897 and 15.2111