Question

Va rooooog .Ma ajuta cineva ,dau multe puncte si coronita,vreau un rasouns pe lung si corect.
Se stie ca 1 supra a-a =8Aflati:
b)a⁴+1supra a⁴

Answer 1

   
[tex]\displaystyle\\ \frac{1}{a}-a =8~~\Big|~\text{(Ridicam la patrat)}\\\\ \left(\frac{1}{a}-a\right)^2=8^2\\\\ \frac{1}{a^2}-2\times\frac{1}{a}\times a+a^2=8^2\\\\ \frac{1}{a^2}-2\times\frac{a}{a}+a^2=64\\\\ \frac{1}{a^2}-2 +a^2=64\\\\ \frac{1}{a^2}+a^2=64+2\\\\ \boxed{a^2+\frac{1}{a^2}=66}~\text{Rezultat intermediar.}\\\\\\ a^2+\frac{1}{a^2}=66~\Big|~\text{(Ridicam la patrat)}\\\\ \left(a^2+\frac{1}{a^2}\right)^2=66^2\\\\ a^4 +2\times a^2\times\frac{1}{a^2}+\frac{1}{a^4}=4356 [/tex]

[tex]\displaystyle\\ a^4 +2\times \frac{a^2}{a^2}+\frac{1}{a^4}=4356\\\\ a^4 +2+\frac{1}{a^4}=4356\\\\ a^4 +\frac{1}{a^4}=4356-2\\\\ \boxed{\boxed{a^4 +\frac{1}{a^4}=4354}}~~~\text{Rezultat final} [/tex]