If a + b + 1 = 0, then the value of (a3 + b3 + 1 – 3ab) is:radio_button_unchecked3radio_button_unchecked0radio_button_unchecked1radio_button_unchecked-1
Question
If a + b + 1 = 0, then the value of (a³ + b³ + 1 – 3ab) is:
- radio_button_unchecked 3
- radio_button_unchecked 0
- radio_button_unchecked 1
- radio_button_unchecked -1
Solution
The given equation is a + b + 1 = 0.
We can rearrange this equation to find that a + b = -1.
The expression we want to find the value of is a^3 + b^3 + 1 - 3ab.
This expression can be rewritten as (a + b)^3 - 3ab(a + b) + 1.
Substituting a + b = -1 into this expression, we get (-1)^3 - 3*(-1)*ab + 1.
This simplifies to -1 + 3ab + 1.
Further simplifying, we get 3ab.
Since we don't know the values of a and b, we can't find the exact value of 3ab.
Therefore, the value of the expression a^3 + b^3 + 1 - 3ab cannot be determined from the given information.
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