Question

The geometric mean of x+3 and 4x+1 is 2x+1. Find all possible values of x.

Answer 1

`x = - (2)/(9)`

Explanation:

Since, the geometric mean of x+3 and 4x+1 is 2x+1.

Therefore, by geometric mean theorem:

`{(2x + 1)}^(2) = (x + 3)(4x + 1) \\ \\ \cancel{4 {x}^(2)} + 4x + 1 = \cancel{4 {x}^(2)} + x + 12x + 3 \\ \\ 4x + 1 = 13x + 3 \\ \\ 4x - 13x = 3 - 1 \\ \\ - 9x = 2 \\ \\ x = - (2)/(9)`