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Ex mate clasa a 10 a : 

    1. [tex] \sqrt[3]{3x+2} = 2[/tex]
    2. [tex] \sqrt{x-2} + x = 4 [/tex]
    3. [tex] 5^{2} = \frac{1}{25} [/tex]
    4. [tex] 2^{x} + 2^{x+1} = 12
[/tex]
    5. [tex] 9^{x} + 3^{x} = 12[/tex]
    6. [tex] log_{5} ( 2x-1 ) = 2[/tex]
    7. [tex] log_{ 2^{x} } + log_{2} (x+2) = 3[/tex]
    8. [tex] log_{3} (x+1 ) - log_{3} (x-1 ) = 1[/tex]

Răspuns :

Dianaangel7ask
1. [tex] (\sqrt[3]{3x+2})^{3} = 2^{3} => 3x+2=8 =>3x=6/:3=> x=2[/tex]
2.[tex] \sqrt{x-2} =4-x=> (\sqrt{x-2})^{2} = (4-x)^{2} => x-2=16-8x+ x^{2} [/tex]=>[tex] x^{2} -9x+18[/tex]
Δ=[tex] b^{2} -4ac=81-72=9[/tex]
[tex] x_{1,2} = \frac{-b+- \sqrt{delta} }{2a} => x_{1,2} = \frac{9+-3}{2} => \left \{ {{ x_{1} =6} \atop { x_{2} =2}} \right. [/tex]
3.Cred ca ai gresit, aia nu e ecuatie.
4. [tex] 2^{x} +2^{x+1} = 3* 2^{2} => x+x+1=2=> 2x=1=> x= \frac{1}{2} [/tex]
5.[tex] 3^{2x} + 3^{x} =3* 2^{2} => 2x+x=1=> 3x=1=> x= \frac{1}{3} [/tex]
6. [tex]2x-1= 5^{2} => 2x=26=> x=13[/tex]
7. [tex] \frac{x}{x+2} =8=> x=8x+16=> x=- \frac{16}{7} [/tex]
8.[tex] \frac{x+1}{x-1} =3=>x+1=3x-3=> -2x=-4=>x=2[/tex]

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