Question and Answers Forum

All Questions      Topic List

Number Theory Questions

Previous in All Question      Next in All Question      

Previous in Number Theory      Next in Number Theory      

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+4p+16=−20 p+8=−5⇒p=−13 (22) f(−a)=−56 2a^3 −3a^2 −13ab+20=−56 2a^3 −3a^2 −13ab+76=0...(1) f(a)=0 −2a^3 −3a^2 +13ab+20=0...(2) (1)+(2)⇒−6a^2 =−96 ⇒a=± 4 (1)−(2)⇒4a^3 −26ab+56=0 ⇒b=((2a^3 +28)/(13a)) { ((a=4⇒b=((2.4^3 +28)/(13.4))=((32+7)/(13))=3)),((a=−4⇒b=((2(−4)^3 +28)/(13(−4)))=((32−7)/(13))=((25)/(13)))) :}

$$\left(\mathrm{21}\right){f}\left(\mathrm{2}\right)=−\mathrm{20}\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{16}+\mathrm{4}{p}+\mathrm{16}=−\mathrm{20} \\ $$$$\:\:\:\:\:\:\:\:\:\:{p}+\mathrm{8}=−\mathrm{5}\Rightarrow{p}=−\mathrm{13} \\ $$$$\left(\mathrm{22}\right)\:{f}\left(−{a}\right)=−\mathrm{56} \\ $$$$\:\:\:\:\:\:\:\mathrm{2}{a}^{\mathrm{3}} −\mathrm{3}{a}^{\mathrm{2}} −\mathrm{13}{ab}+\mathrm{20}=−\mathrm{56} \\ $$$$\:\:\:\:\:\:\mathrm{2}{a}^{\mathrm{3}} −\mathrm{3}{a}^{\mathrm{2}} −\mathrm{13}{ab}+\mathrm{76}=\mathrm{0}...\left(\mathrm{1}\right) \\ $$$$\:{f}\left({a}\right)=\mathrm{0} \\ $$$$\:\:−\mathrm{2}{a}^{\mathrm{3}} −\mathrm{3}{a}^{\mathrm{2}} +\mathrm{13}{ab}+\mathrm{20}=\mathrm{0}...\left(\mathrm{2}\right) \\ $$$$\left(\mathrm{1}\right)+\left(\mathrm{2}\right)\Rightarrow−\mathrm{6}{a}^{\mathrm{2}} =−\mathrm{96} \\ $$$$\Rightarrow{a}=\pm\:\mathrm{4} \\ $$$$\left(\mathrm{1}\right)−\left(\mathrm{2}\right)\Rightarrow\mathrm{4}{a}^{\mathrm{3}} −\mathrm{26}{ab}+\mathrm{56}=\mathrm{0} \\ $$$$\Rightarrow{b}=\frac{\mathrm{2}{a}^{\mathrm{3}} +\mathrm{28}}{\mathrm{13}{a}} \\ $$$$\:\begin{cases}{{a}=\mathrm{4}\Rightarrow{b}=\frac{\mathrm{2}.\mathrm{4}^{\mathrm{3}} +\mathrm{28}}{\mathrm{13}.\mathrm{4}}=\frac{\mathrm{32}+\mathrm{7}}{\mathrm{13}}=\mathrm{3}}\\{{a}=−\mathrm{4}\Rightarrow{b}=\frac{\mathrm{2}\left(−\mathrm{4}\right)^{\mathrm{3}} +\mathrm{28}}{\mathrm{13}\left(−\mathrm{4}\right)}=\frac{\mathrm{32}−\mathrm{7}}{\mathrm{13}}=\frac{\mathrm{25}}{\mathrm{13}}}\end{cases} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com