Question

identify the pair of consecutive integers between which the positive geometric mean for 4 and 12 falls between

Answer 1

`\bf \cfrac{4}{x}=\cfrac{x}{12}\impliedby x=\textit{geometric mean}\implies 48=x^2 \\\\\\ √(48)=x\implies 4√(3)=x\implies 6.9\approx x \\\\\\ \boxed{6}\leftarrow 4√(3)\to \boxed{7}`