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

Sagot :

Hrishiiidn

Answer:

[tex] x = - \frac{2}{9} [/tex]

Step-by-step explanation:

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

Therefore, by geometric mean theorem:

[tex] {(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} [/tex]

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