what are the two numbers have a sum of 14 and a product of 40
2 answers
10*4 = 40, 10+4 = 14
Let the numbers be x and y
x+y=14....eqn(i)
xy=40....eqn(ii)
from eqn(i), y=14-x
substitute y=14-x in eqn(ii)
x(14-x)=40
14x-x^2=40
x^2-14x+40=0
solve using factorization method
x^2-4x-10x+40=0
x(x-4)-10(x-4)=0
(x-4)(x-10)=0
x=4 or x=10
when x=4, y=14-4=10
when x=10, y=14-10=4
therefore, the two numbers are 4 and 10
x+y=14....eqn(i)
xy=40....eqn(ii)
from eqn(i), y=14-x
substitute y=14-x in eqn(ii)
x(14-x)=40
14x-x^2=40
x^2-14x+40=0
solve using factorization method
x^2-4x-10x+40=0
x(x-4)-10(x-4)=0
(x-4)(x-10)=0
x=4 or x=10
when x=4, y=14-4=10
when x=10, y=14-10=4
therefore, the two numbers are 4 and 10