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Pe: 2014-02-06T06:46:52+02:00 In: In:

Algebra

Se da expresia E(x)=[(3/4x+5)-(5/4x-5)+(2x+3/16x^2-25)]: (-6x-37/16x^2+40x+25)+2
a)Aduceti expresia la forma cea mai simpla
b)Det valorile lui x pt care expresia nu are valuare definita
c)Det valorile intregi ale lui x pt care E(x) este numar natural
d)Rezolvati ecuatia E(x)=8-(3/4x-5)

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4 raspunsuri

  1. tata2008
    maestru (V)

    Se da expresia E(x)=[(3/4x+5)-(5/4x-5)+(2x+3/16x^2-25)]: (-6x-37/16x^2+40x+25)+2
    a)Aduceti expresia la forma cea mai simpla


    \rm{\bl\\<br/> E(x)=[\frac{3}{4x+5}-(\frac{5}{4x-5}+\frac{2x+3}{16x^2-25})] : (\frac{-6x-37}{16x^2+40x+25}) + 2\\<br/> [ ... ] =\frac{3}{4x+5}-\frac{5}{4x-5}+\frac{2x+3}{\underbrace{16x^2-25}_{(4x-5)(4x+5)}}=\\<br/> =\frac{3(4x-5)-5(4x+5)+2x+3)}{(4x-5)(4x+5)}=\frac{-6x-37}{(4x-5)(4x+5)}\surd\surd\\<br/> (...)=\frac{-6x-37}{\underbrace{16x^2+40x+25}_{(4x+5)^2})}\surd\surd\\<br/> [...]<E>:(</E>...) = \frac{-6x-37}{(4x-5)(4x+5)} \cdot \frac{(4x+5)^2}{-6x-37}=\fbox{\frac{4x+5}{4x-5}} <br/> <br/> <br/> <br/>

  2. tata2008
    maestru (V)

    …

  4. tata2008
    maestru (V)

    b)Det valorile lui x pt care expresia nu are valuare definita


    \rm{\bl\\ E(x)=\frac{4x+5}{4x-5} nu este definita daca 4x-5=0 deci \fbox{x=\frac{5}{4}=1,25}\\

    c)Det valorile intregi ale lui x pt care E(x) este numar natural


    \rm{\bl\\E(x)=\frac{4x+5}{4x-5} \in \mathbb{N} daca (4x-5) | (4x+5)\\ E(x)=\frac{4x+5}{4x-5}=\frac{4x-5+10}{4x-5}=\underbrace{\frac{4x-5}{4x-5}}_{\in \mathbb{N}}+\underbrace{\frac{10}{4x-5}}_{\in \mathbb{N} daca (4x-5) | 10}\\ \Rightarrow 4x-5 \in \{-10;-5;-2;-1;1;2;5;10\} verificand fiecare caz in parte se va obtine x= .... ;

  5. tata2008
    maestru (V)

    d)Rezolvati ecuatia E(x)=8-(3/4x-5)

    \rm{\bl\\ \Rightarrow \frac{4x+5}{4x-5} = ^{^{4x-5)}}8-\frac{3}{4x-5}\\ 4x+5=32x-40-3 \Leftrightarrow x=\frac{12}{7}

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