Question

cum se demonstreaza ca 2 la putere x + 2 la puterea minus x este egal cu 5 supra 2 ?

 

Answer 1

[tex] 2^{x} + 2^{-x} = \frac{5}{2} 2^{x} + \frac{1}{ 2^{x} } = \frac{5}{2} [/tex]
$\frac{ 2^{2x}+1 }{ 2^{2x} } = \frac{5}{2}$
$2* 2^{x} +2=5* 2^{x}$
notam $2^{x} =t$
2t²-5t+2=0
Δ=25-4*2*2=9
t₁₂=(5+-√9)/4
t₁=2⇒$2^{x} = 2^{1}$⇒x=1
t²=1/2⇒$2^{x} = 2^{-1}$⇒x=-1