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Se stie ca 1/a-a=8 . Aflati 1) a² + 1/a². 2) a⁴ + 1/a⁴ 

Răspuns :

[tex]\dfrac{1}{a}-a=8 |()^2\\ \left(\dfrac{1}{a}-a\right)^2=64\\ \dfrac{1}{a^2}-2+a^2=64\\ \boxed{\dfrac{1}{a^2}+a^2=66}[/tex]
[tex]\left(\dfrac{1}{a^2}+a^2\right)^2=4356\\ \dfrac{1}{a^4}+a^4+2=4356\\ \boxed{\dfrac{1}{a^4}+a^4=4354}[/tex]

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