Question

Sa se rezolve in R ecuația :
${(1 + \sqrt{2)} }^{x} -{( \sqrt{2 } - 1) }^{x} = \frac{3}{2}$

Answer 1

se observa ( !!!??????!!) ca 1/(1+√2)=√2-1

atunci (√2-1)^x=1/(√2-1)^x

atunci, notand cu ( 1+√2)^x=y

y-1/y=3/2

2y-2/y=3

2y²-3y-2=0

y1,2=(3+-√25)/4

y1=-1/2<0, x∈∅

y2=(3+5)/4=2

(1+√2)^x=2

x= logaritm in baza (1+√2) din 2