If alpha plus beta equals to 3 and alpha cube plus beta cube equals to 7,then alpha and beta are the roots of equation

[tex] \alpha + \beta = 3\\ \alpha ^3 + \beta ^3 = 7\\\\ \alpha ^3 + \beta ^3 = 7\\( \alpha + \beta )( \alpha ^2 + \beta ^2 - \alpha \beta ) = 7\\\alpha ^2 + \beta ^2 - \alpha \beta = \frac{7}{3}\\( \alpha + \beta )^2 - 3 \alpha \beta = \frac{7}{3}\\3 \alpha \beta = 9 - \frac{7}{3}\\3 \alpha \beta = \frac{20}{3} \\ \alpha \beta = \frac{20}{9}\\\\So....\\x^2 - ( \alpha + \beta )x + ( \alpha \beta ) = 0\\x^2 - 3x + \frac{20}{9} = 0\\\boxed{\boxed{9x^2 - 27x + 20 = 0}}[/tex]

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Alpha = a
Beta = b

a + b = 3
a³ + b³ = 7

Ingat , pemfaktoran dr a³ + b³
= (a + b)(a² - ab + b²)

7 = 3(a² + b² - ab)

(a + b)² = a² + 2ab + b²
(a + b)²- 2ab = a² + b²

-->
7 = 3( (a +b)² - 2ab - ab))
7 = 3 ( 3² - 3ab)
7 = 3(9 - 3ab)
7 = 27 - 9ab
9ab = 27-7
9ab = 20
ab = 20/9

Krn akar akarnya alfa dan beta , maka disusun PK sbg :
x² - (a + b)x + (ab) = 0
x² - 3x + 20/9 = 0
Kali 9 kdua ruas

9x² - 27x + 20 = 0