Question

what are 2 numbers that add to 16 and multiply to 10

Answer 1

find multipules of 10
1 and 10
2 and 5
1+10=11 NO
2+5=7 ono

so do
x+y=16
xy=10

x+y=16
subtract x from both sides
y=16-x
subsitute
x(16-x)=10
distribute
16x-x^2=10
add x^2 to btoh sides
16x=x^2+10
subtrac 16 x from oth sies
0=x^2-16x+10
use quadratic formula which is
x=$\frac{-b+/- \sqrt{ b^{2}-4ac } }{2a}$ when you have
0=ax^2+bx+c

0=x^2-16+10
a=1
b=-16
c=10
subsitute
x=$\frac{-(-16)+/- \sqrt{ (-16)^{2}-4(1)(10) } }{2(1)}$
x=$\frac{16+/- \sqrt{ 256-40 } }{2}$
x=$\frac{16+/- \sqrt{ 216 } }{2}$
x=$\frac{16+/- 6\sqrt{6 } }{2}$
x=$8+/- 3\sqrt{6}$
x=8+$3 \sqrt{6}$ or 8-$3 \sqrt{6}$
aprox
x=15.3485 or 0.651531
so thos are the 2 numbers