Question

a+b= -13., ab=26, what are a and b

Answer 1

hi

given equation
a+b= -13
ab= 26

from equation a+b=-13
can be written as a= -13-b
substitute in ab= 26
(-13-b)b= 26
multiple
-13b-b²=26
-13b-b²-26=0
take (-) common
b²+13b+26=0

now find factors

formula=( -b±√ (b²-4ac))/2a
from above when compared to standard equation ax²+bx+c=0
then a=1;b=13;c=26
substitute in above formula

then b= (-13±√65)/2

substitute in any one of the given equation we get same answer
now I am going to substitute in a+b=-13 equation

a+(-13±√65)/2=-13
a = -13-(-13±√65)/2
a= -(13±√65)/2

therefore
a= -(13±√65)/2
b= (-13±√65)/2