If #m+n=7# and #m^2+n^2=29#, find the two numbers?

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Answer 1 · 2018-02-14T09:13:50

Two numbers are #2# and #5#.

As #m+n=7#, #m=7-n#

Now substituting this value of #m# in other equation, we get

#(7-n)^2+n^2=29#

or #49-14n+n^2+n^2=29#

or #2n^2-14n+20=0#

or #n^2-7n+10=0#

or #(n-2)(n-5)=0#

i.e. #n=2# or #n=5#

Observe that when #n=2#, we have #m=5# and

when #n=5#, we have #m=2#

i.e. the two numbers are #2# and #5#.