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Stiind ca 5a-2b pe 2a+b = 1pe4, calculati a pe b

Răspuns :

Andreutzakriss
5a-2b/2a+b=1/4=>20a-8b=2a+b
19a=9b
a/b=18/9
a/b=2
Bafta la scoala!
[tex]\dfrac{5a-2b}{2a+b} = \dfrac{1}{4} \Leftrightarrow 4(5a-2b)=1(2a+b) \Leftrightarrow 20a-8b = 2a+b \\\;\\ \Leftrightarrow 20a-2a=b+8b \Leftrightarrow 18a = 9b|_{ :b} \Leftrightarrow \dfrac{18a}{b}=9|_{ :18} \Leftrightarrow \\\;\\ \Leftrightarrow \dfrac{a}{b} = \dfrac{9}{18} \raisebox{2.8ex}{(9}\Leftrightarrow \dfrac{a}{b} = \dfrac{1}{2} [/tex]

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