Question

Sa se rezolve ecuatiile ( exponentiale )
a) $( \sqrt{5} + 2)^{2} + (\sqrt{5}-2)^{x} = 18$

Answer 1

(√5+2)*(√5-2)=1=>
√5-2=1/(√5+2)
(√5+2)²+1/(√5+2)^x=18
Notezi (√5+2)^x=y  y>0
(√5+2)²+1/y=18
(5+4√5+4)y+1=18y
1=18y-9y-4√5y
1=(9-4√5)*y
1=(√5-2)²*y
1=y/(√5+2)²=>
y=(√5+2) ² Revii  la  substitutie
(√5+2)^x=(√5+2)^2 =>x=2