Question

the square root of 12 is the geometric mean between x and y. find x if y = the square root of 3. thanks!!

Answer 1

`\bf \cfrac{x}{\textit{geometric mean}}=\cfrac{\textit{geometric mean}}{y}\implies \cfrac{x}{√(12)}=\cfrac{√(12)}{√(3)}\implies \cfrac{x}{√(12)}=\cfrac{√(4\cdot 3)}{√(3)} \\\\\\ \cfrac{x}{√(12)}=\cfrac{√(4)√(3)}{√(3)}\implies \cfrac{x}{√(12)}=√(4)\implies \cfrac{x}{√(12)}=2\implies x = 2√(12) \\\\\\ x = 2√(4)√(3)\implies x=2\cdot 2√(3)\implies x=4√(3)`