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Alexutzaa1Alle
a fost răspuns

Stiind ca a+1/a=4,a≠0,calculeaza a²+1/a²

Răspuns :

Albatran
a²+(1/a)²=(a+1/a)²-2*a*1/a=4²-2=16-2=14

[tex]\it a+\dfrac{1}{a} = 4 \Rightarrow \left(a+\dfrac{1}{a}\right)^2 = 4^2 \Rightarrow a^2+ 2\cdot a \cdot \dfrac{1}{a} +\left(\dfrac{1}{a}\right)^2 = 16\Rightarrow \\\;\\ \\\;\\ \Rightarrow a^2+2+ \dfrac{1}{a^2} =16 |_{-2} \Rightarrow a^2 + \dfrac{1}{a^2} = 14 [/tex]


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