SOLUTION: There are two triples of positive integers (a,b,c and d,e,f) such that a�+b�+c�=86 and d�+e�+f�=86. Evaluate the expression absolute value of abc-def.

Question 1106473: There are two triples of positive integers (a,b,c and d,e,f) such that
a�+b�+c�=86 and d�+e�+f�=86. Evaluate the expression absolute value of
abc-def.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
There are two triples of positive integers (a,b,c and d,e,f) such that
a�+b�+c�=86 and d�+e�+f�=86. Evaluate the expression absolute value of
------------------
Obviously, all are less than 10.
There's no algebraic solution, just trial and error.
There's no reason for me to do it.
You do it.
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.

1) 86 = 1^2 + 2^2 + 9^2 2) 86 = 5^2 + 5^2 + 6^2. You do the rest.

RELATED QUESTIONS
There are two triples of positive integers (a,b,c and d,e,f) such that {{{ a^2+b^2+c^2=86 (answered by ikleyn)
There are two triples of positive integers (a,b,c and d,e,f) such that a^2+b^2+c^2 = 86... (answered by Edwin McCravy,ikleyn)
There are 3 different triples of(not necessarily distinct) positive integers(a,b,c, d,e,f (answered by ikleyn)
There are two differnet triples of positive integers (a,b,c) and (d,e,f) such that a^2 +... (answered by ikleyn,greenestamps)
There are three triples of positive integers (a,b,c, d,e,f and g,h,i) such that a^2 +... (answered by ikleyn)
There are three triples of positive integers (a,b,c, d,e,f, and g,h,i) such that... (answered by ikleyn,Edwin McCravy)
What is the smallest value of f that satisfies {{{ a^2+b^2+c^2+d^2+e^2=f^2 }}}, given... (answered by Alan3354,Edwin McCravy)
What is the smallest value of {{{ f }}} that statisfies {{{ a^2+b^2+c^2+d^2=f^2 }}},... (answered by ankor@dixie-net.com)
The numbers a,b,c,d,e,f,g are positive consecutive integers in increasing order. Given (answered by Alan3354)