Question-157853

Question Number 157853 by emanuelMcCarthy last updated on 28/Oct/21

Commented by cortano last updated on 29/Oct/21

(21) f (2) = - 20

16 + 4 p + 16 = - 20

p + 8 = - 5 \Rightarrow p = - 13

(22) f (- a) = - 56

2 a^{3} - 3 a^{2} - 13 a b + 20 = - 56

2 a^{3} - 3 a^{2} - 13 a b + 76 = 0 \dots (1)

f (a) = 0

- 2 a^{3} - 3 a^{2} + 13 a b + 20 = 0 \dots (2)

(1) + (2) \Rightarrow - 6 a^{2} = - 96

\Rightarrow a = \pm 4

(1) - (2) \Rightarrow 4 a^{3} - 26 a b + 56 = 0

\Rightarrow b = \frac{2 a^{3} + 28}{13 a}

{\begin{cases} a = 4 \Rightarrow b = \frac{2 . 4^{3} + 28}{13.4} = \frac{32 + 7}{13} = 3 \\ a = - 4 \Rightarrow b = \frac{2 {(- 4)}^{3} + 28}{13 (- 4)} = \frac{32 - 7}{13} = \frac{25}{13} \end{cases}

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