Question

Sa se determine valorile reale ale numărului stiind ca numerele x-3;4si x+3 sunt termeni consecutivi ai unei progresii geometrice​

Answer 1

 

$\displaystyle\bf\\x-3;~4;~x+3~~\text{sunt termeni consecutivi  ai unei progresii geometrice.}\\\\\implies~\frac{4}{x-3}=\frac{x+3}{4}\\\\(x-3)(x+3)=4\cdot4\\\\x^2-9=16\\\\x^2-9-16=0\\\\x^2-25=0\\\\{x-5}(x+5)=0\\\\\boxed{x_1=5}\implies~progresia\!: ~~\{5-3;~4;~5+3\}=\boxed{\bf\{2;~4;~8\}}\\\\\boxed{x_2=-5}\implies~progresia\!: ~~\{-5-3;~4;~-5+3\}=\boxed{\bf\{-8;~4;~-2\}}$