Question

Ecuaţia (5^x + m2^x)/(2^x - m5^x) = 2 admite soluţii pentru m ∈(?)

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

$\it Notez\ 5^x=a,\ \ 2^x=b,\ \ a,b>0,\ iar\ acum\ ecua\c{\it t}ia\ devine:\\ \\ \dfrac{a+bm}{b-am}=2 \Rightarrow a+bm=2b-2am \Rightarrow a+2am=2b-bm \Rightarrow \\ \\ \Rightarrow a(1+2m)=b(2-m) \Rightarrow \dfrac{a}{b}=\dfrac{2-m}{1+2m}\ \ \ \ (*)$

$\it a,\ b>0 \Rightarrow \dfrac{a}{b}>0 \stackrel{(*)}{\Longrightarrow}\ \dfrac{2-m}{1+2m} >0 \Rightarrow m\in \Big(-\dfrac{1}{2},\ \ 2\Big)$