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Question 14
a, b, c are integers, |a| ≠ |b| ≠|c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc - (a + b + c)]?
Solution
|a| ≠ |b| ≠|c| and -10 ≤ a, b, c ≤ 10
Expression : $$[abc - (a + b + c)]$$
For maximum value, two of a,b and c should be negative, as all three negative will make abc negative.
Thus, max value will occur if $$a = -10 , b = -9 , c = 8$$
=> Max value = $$[(-10 \times -9 \times 8) - (-10 -9 + 8)]$$
= $$720 + 11 = 731$$
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