2positive integers have a sum of 10 and a product of 21, what are the integers?

1 Answer
May 15, 2018

Answer:

#x=3# or #x=7#
#y=7# or #y=3#

Explanation:

Lets say two positive integers are #x# and #y#.

So #x+y = 10# and #x xx y = 21#

We have two equations here:
#x + y = 10# ----> equation 1
#xy = 21# ----> equation 2

From equation 1, make #y# the subject.

#x + y = 10#
#y = 10-x# --- substitute #y# in equation 2

#xy = 21# ---- Equation 2

#x(10-x) = 21 #10x-x^2 = 21#

Re-arranging the equation, we get:
#-x^2+10x-21=0#

Lets solve for #x# now:

#-x^2+10x-21=0#

Multiply by (#-1#) throughout and we get:

#x^2-10x+21=0#

Factors are #-3# and #-7# as #-3 + -7=10# and #-3 xx (-7) = 21#

#x^2-10x+21=0#
#x^2-3x-7x+21=0#
#x(x-3)-7(x-3)=0#
#(x-7)(x-3)=0#

Hence, #x=7# or #x=3#

Substitute value of #x#in equation 1

Take #x=7#
#7 + y = 10#
#y=10-7#
#y=3# -----> First value of #y#

Take #x=3#

#3 + y = 10#
#y=10-3#
#y=7# ------> Second value of #y#

Therefore Answer is:

#x=3# or #x=7#
#y=7# or #y=3#

And all of them are positive.