Question

Evalute 3n² - 8n - 9, given n(n - 3) = 10.​

Answer 1

19 or 26

Explanation:

You want the value of 3n² -8n -9, given that n(n -3) = 10.

Values of n

We recognize that 10 = 5·2 and that these factors differ by 3. This means n(n -3) = 10 is equivalent to saying n ∈ {-2, 5}.

Expression in n

The value of 3n² -8n -9 will be one of ...

(3n -8)n -9 = (3(-2) -8)(-2) -9 = (-14)(-2) -9 = 19 . . . . for n = -2

or

(3(5) -8)(5) -9 = (7)(5) -9 = 26 . . . . . . . for n = 5

The expression 3n² -8n -9 will be either 19 or 26.

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