Question

Am nevoie de putin ajutor la aceste exercitii...
Ma poate ajuta cineva, va rog?
Multumesc anticipat! :)
$( { \sqrt{5} - 2)}^{x} + ( { \sqrt{5 } + 2)}^{x} = 18 \\ 3 \times {4}^{2x + 1} - 25 \times {12}^{x} + 4 \times {3}^{2x + 1} = 0$

Answer 1

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Answer 2

1) fie $( \sqrt{5}-2)^x=a,a\ \textgreater \ 0 \\ a+ \frac{1}{a}=18 \\ a^{2}-18a+1=0$
Δ=324-4=320
$a_{1}= \frac{18-8 \sqrt{5} }{2} =9-4 \sqrt{5} \\ a_{2}=9+ \sqrt{5}$
revenim la substitutie
$( \sqrt{5}-2)^x=(2+ \sqrt{5})^2 \\ x=-2$