Question 1158007
General term of the progression, {{{A[1]+d(n-1)}}}


Your description:
{{{system(A[1]+d*(0)+A[1]+d+A[1]+2d=42,A[1]*(A[1]+2d)=52)}}}.
Linear system of two unknown variables.
Work with those.


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{{{system(3A+3d=42,A^2+2Ad=52)}}}


{{{system(3(A+d)=42,A^2+2Ad=52)}}}


{{{system(A+d=14,A^2+2Ad=52)}}}


{{{d=14-A}}}
substitute
{{{A^2+2A(14-A)=52}}}

{{{A^2+28A-2A^2=52}}}

{{{-A^2+28A-52=0}}}

{{{A^2-28A+52=0}}}

{{{(A-26)(A-2)=0}}}

A is 24  or A is 2.


Finding d
d=14-A
If A is 2 then {{{d=12}}}
OR
If A is 24 then {{{d=14-24=-10}}}


Using the positive difference d, the three numbers are:
2, 14, 26