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ksoodagoat
22.11.2019 •
Mathematics
Solve the following equation:
9n² - n - 2/3 = 0
Solved
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Ответ:
see explanation
Step-by-step explanation:
Given
9n² - n -
= 0 ← multiply through by 3 to clear the fraction
27n² - 3n - 2 = 0 ← factoring
Consider the factors of the product of the n² term and the constant term which sum to give the coefficient of the n- term
product = 27 × - 2 = - 54 and sum = - 3
The factors are - 9 and + 6
Use these factors to split the n- term
27n² - 9n + 6n - 2 = 0 ( factor the first/second and third/fourth terms )
9n(3n - 1) + 2(3n - 1) = 0 ← factor out (3n - 1) from each term
(3n - 1)(9n + 2) = 0
Equate each factor to zero and solve for n
3n - 1 = 0 ⇒ 3n = 1 ⇒ n =![\frac{1}{3}](/tpl/images/0386/5429/5506e.png)
9n + 2 = 0 ⇒ 9n = - 2 ⇒ n = -![\frac{2}{9}](/tpl/images/0386/5429/746ea.png)
Ответ: