One integer is 3 less then another. The sum of their squares is 185. Find the integers?

1 Answer
Apr 18, 2018

I tried this:

Explanation:

Let us call the two integers #a and b#; we get:

#a=b-3#
#a^2+b^2=185#

substitute the first into the second:

#(b-3)^2+b^2=185#

#b^2-6b+9+b^2=185#
#2b^2-6b-176=0#
solve using the Quadratic Formula:

#b_(1,2)=(6+-sqrt(36+1408))/4=(6+-38)/4#

so we get:

#b_1=(6+38)/4=11#
and:
#b_2=(6-38)/4=-8#

So we get two options:
Either:
#b=11# and #a=11-3=8#
Or:
#b=-8# and #a=-8-3=-11#