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Question Number 191030 by cortano12 last updated on 16/Apr/23

Answered by Frix last updated on 16/Apr/23

$$t+\frac{1}{t}=3$$$${(t+\frac{1}{t})}^2=9\iff t^2+\frac{1}{t^2}=7$$$${(t+\frac{1}{t})}^3=27\iff t^3+\frac{1}{t^3}=18$$$$E=\sqrt{\frac{(t^3+t^2)(t^5+1)}{t^5}}=\sqrt{\frac{t^8+t^7+t^3+t^2}{t^5}}=$$$$=\sqrt{t^3+\frac{1}{t^3}+t^2+\frac{1}{t^2}}=\sqrt{18+7}=\sqrt{25}=5$$

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