Andreea2022ask
a fost răspuns

daca a supra b = 3 - √5 , sa se calculeze raportul  a² + b² supra ab
 
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Răspuns :

Tstefanask
[tex] \frac{a}{b} =3- \sqrt{5} [/tex]

[tex] \frac{ a^{2}+b^{2}}{ab}= \frac{ a^{2}}{ab}+\frac{ b^{2}}{ab}= \frac{a}{b}+\frac{b}{a}=\frac{a}{b}+ \frac{1}{\frac{a}{b}}= 3- \sqrt{5}+ \frac{1}{3- \sqrt{5}}= \frac{15-6 \sqrt{5} }{3- \sqrt{5}} [/tex]
Bunicaluiandreiask


a/b=3-√5     a=(3-√5)·b             a²=(9-6√5+5)·b²=(14-6√5)·b²                                  a²+b²=b²(14-6√5+1)=(15-6√5)b²         a·b=(3-√5)·b²

(a²+b²)/ab=3(5-2√5)b²/(3-√5)b²=3

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