The sum of the squares of two positive numbers is 80 and the difference of the squares of the numbers is 48. How do you find the numbers?

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Answer 1 · 2018-07-11T17:31:45

I got #8 and 4#

Let us call the numbers #x# and #y# we get:

#x^2+y^2=80#

#x^2-y^2=48#

let us add the two together:

#(x^2+x^2)+(y^2-y^2)=80+48#

#2x^2=128#

#x^2=128/2=64#

#x=+-sqrt(64)=+-8# Let us choose the positive one and substitute into the first equation for #x#:

#8^2+y^2=80#

#y^2=80-64=16#

#y=+-sqrt(16)=+-4# let us choose again the positive one.