Find values A, B, C, such that A + B + C = ABC = 1, and that the largest absolute value of A, B, or C is at a minimum. For example, the largest absolute value of -1, 1/3, or-3 would be 3. But -1 + 1/3 - 3 does not add up to 1, nor 3 is the minimum possible.
2007-01-24 13:58:37 · 1 answers · asked by Scythian1950 7 in Science & Mathematics ➔ Mathematics
Too bad I can't give more than 10 points for this one.
2007-01-24 14:11:08 · update #1
Real values for A, B, C only, no complex numbers.
2007-01-24 14:52:36 · update #2
tablecloth, good start, but the maximum absolute value of the A, B,C you've given is still 3. I believe a lower value is possible.
2007-01-24 16:06:18 · update #3
A+B+C=1
ABC=1
so neither of them can be =0.
so A = 1/BC
1/BC + B + C =1
1+ B^2C + BC^2 =BC
say it is an equation on B:
B^2 C + B( C^2 -C) +1 =0
B= ( C-C^2 +- sqrt( ( C^2-C)^2 -4C) )/2C
C=3: B = ( 3-9 +- sqrt ( 36 -12) ) /6 = ( -9 +- sqrt(24) )/6
A= 1/3( -9 + sqrt(24) )/6 = 2/( -9 + sqrt(24) .
2007-01-24 15:36:35 · answer #1 · answered by tablecloth 1 · 2⤊ 0⤋