Question 983136

Let &nbsp;<B>x</B>&nbsp; be the first unknown integer and &nbsp;<B>y</B>&nbsp; be the second unknown integer.

Then you have two equations


{{{system(x = 6y + 10,
xy = 464)}}}. 


To solve the system, &nbsp;substitute the first equation into the second one. &nbsp;You will get


(6y + 10)*y = 464.


Simplify and solve it:


{{{6y^2}}} + {{{10y}}} = {{{464}}},


{{{6y^2}}} + {{{10y}}} - {{{464}}} = {{{0}}},


{{{y[1]}}} = {{{(-10 + sqrt(10^2 + 4*6*464))/12}}} = {{{(-10 + 106)/12}}} = {{{96/12}}} = {{{8}}},


{{{y[2]}}} = {{{(-10 - sqrt(10^2 + 4*6*464))/12}}} = {{{(-10 - 106)/12}}} = {{{(-116)/12}}} = {{{9}}}{{{2/3}}}.


Only first root satisfies the condition of the problem &nbsp;(is integer).


<B>Answer</B>. &nbsp;The two integers are &nbsp;8&nbsp; and &nbsp;6*8+10 = 58.