Question

Sa se determine x>0 stiind ca numerele x+1; 6; x+10 sunt in progresia geometrica

Answer 1

Răspuns:

$6=\sqrt{(x+1)(x+10)}\\6^2=(x+1)(x+10)\\36=x^2+10x+x+10\\x^2+11x-26=0\\\Delta=225\Rightarrow \sqrt{\Delta}=15\\\\x_{1,2}=\displaystyle\frac{-11\pm15}{2}\\\\x_1=-13<0\\x_2=2>0\Rightarrow x=2$

Explicație pas cu pas: