Question 1209465
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There are two {{{highlight(cross(differnet))}}} <U>different</U> triples of positive integers (a,b,c) and (d,e,f) such 
that a^2 + b^2 + c^2 = 90 and d^2 + e^2 + f^2 = 90. Find the sum a+b+c+d+e+f.
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There are two basic triples (a,b,c) and (d,e,f) of positive integer numbers such that

    a^2 + b^2 + c^2 = 90,

    d^2 + e^2 + f^2 = 90.


These triples are  (a,b,c) = (8,5,1)  and  (d,e,f) = (7,5,4).


All other triples of this kind are permutations of these triples.


Permutations do not change the sum  a+b+c+d+e+f,  therefore, this sum has a uniques value

    a + b + c+ d + e + f = 8 + 5 + 1 + 7 + 5 + 4 = 30.


<U>ANSWER</U>.  The sum  a + b + c+ d + e + f  is  30.
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Solved.