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Aloiza [94]
3 years ago
14

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

Mathematics
1 answer:
Anastaziya [24]3 years ago
4 0

Answer:

x =   - \frac{2}{9}

Step-by-step 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 =   - \frac{2}{9}

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