Question

The sum of a number and 3 times its reciprocal is – 4. Find the number(s).

Answer 1

Answer:

Step-by-step explanation:

Let the number be x,

Reciprocal of x = 1/x  

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Four times of x = 4x

3 times its reciprocal = 3/x

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ATQ,

4x + 3/x = 7  

4x² + 3 = 7x  

4x² - 7x + 3 = 0

4x² - (4 + 3)x + 3 = 0  

4x² - 4x - 3 x  + 3 = 0  

4x( x - 1) - 3(x - 1)  = 0  

(x -1 ) (4x - 3) = 0  

x = 1   Or   x = 3/4  

number can be 1 or can be 3/4

Answer 2

Given,

$\[x + \frac{3}{x} = - 4\]$

Solution,

Calculate the number.

$\[x + \frac{3}{x} = - 4\]$

$\[\begin{array}{l} \Rightarrow {x^2} + 3 = - 4x\\ \Rightarrow {x^2} + 4x + 3 = 0\\ \Rightarrow {x^2} + 3x + x + 3 = 0\\ \Rightarrow x\left( {x + 3} \right) + 1\left( {x + 3} \right) = 0\\ \Rightarrow \left( {x + 3} \right)\left( {x + 1} \right) = 0\\ \Rightarrow x = - 1, - 3\end{array}\]$

Hence the number is $\[ - 1, - 3\]$.