mg este media proporțională a numerelor a și b

[tex]\bf m_g = \sqrt{a \cdot b}[/tex]

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[tex]a = 1 \dfrac{11}{21} = \dfrac{21+11}{21} = \dfrac{32}{21}[/tex]

[tex]m_g = 1 \dfrac{5}{7} = \dfrac{7+5}{7} = \dfrac{12}{7}[/tex]

[tex]m_g^2 = a \cdot b \Rightarrow \bigg( \dfrac{12}{7}\bigg)^2 = \dfrac{32}{21} \cdot b \Rightarrow \dfrac{12^2}{7^2} = \dfrac{32}{21} \cdot b \Rightarrow b = \dfrac{12^2 \cdot 21}{7^2 \cdot 32}[/tex]

[tex]\Rightarrow \bf b = \dfrac{27}{14}[/tex]

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[tex]a = 0,1 = \dfrac{1}{10}[/tex]

[tex]m_g = 0,11 = \dfrac{11}{100}[/tex]

[tex]m_g^2 = a \cdot b \Rightarrow \bigg( \dfrac{11}{100}\bigg)^2 = \dfrac{1}{10} \cdot b \Rightarrow \dfrac{121}{10000} = \dfrac{1}{10} \cdot b \Rightarrow b = \dfrac{121 \cdot 10}{10000}[/tex]

[tex]\Rightarrow \bf b = \dfrac{121}{1000} = 0,121[/tex]