SOLUTION: Dear Sir As a 72 year old, interested in numbers and algebra, but with very limited knowledge on the subject, I have been trying to algebraically solve the following problems, rat

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Question 54056: Dear Sir
As a 72 year old, interested in numbers and algebra, but with very limited knowledge on the subject, I have been trying to algebraically solve the following problems, rather than by trial and error or a process of elimination.
abc=a+b+c, 1x2x3=1+2+3=6
abc=(a+b+c)² 8x16x72=(8+16+72)² 9216=96²
abcd=(a+b+c+d)² 2x4x6x12=(2+4+6+12)² 576=24²
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
abc+=+a%2Bb%2Bc
abc+-+c+=+a%2Bb
c%28ab+-+1%29+=+a%2Bb
c+=+%28a%2Bb%29%2F%28ab+-+1%29
I will choose values for a and b arbitrarily. Suppose a = 6 and b = 2:
c+=+8%2F11
6%2B2%2B8%2F11+=+6%2A2%2A8%2F11
Therefore, we can choose any value for two of the values, and find a value for which this equation is true.
Similarly with all the other equations, as long as you don't restrict them to the naturals, and algebra isn't capable of that.