# The product of seven and a number, reduced by 2 equals triple the same number, raised by 4. How do you find the number?

Jan 12, 2017

Is this question correct? should it read "raised by 2"?

#### Explanation:

Taken literally, what you have written can be interpreted in two ways.

First interpretation: $7 x - 2 = 3 {x}^{4}$
Second interpretation: $7 x - 2 = {\left(3 x\right)}^{4}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Assumption: the question means $\text{ } 7 x - 2 = 3 {x}^{4}$

$\implies 3 {x}^{4} - 7 x + 2 = 0$

Using iteration method:

Write as $x \left(3 {x}^{3} - 7\right) = - 2$

$\implies x = - \frac{2}{3 {x}^{3} - 7}$

Set the seed value for $x$ as 0.5

$0.301886 \ldots .$
$0.289123 \ldots .$
$0.288704 \ldots$
$0.2886915 \ldots .$
$0.2886911 \ldots . . \leftarrow \text{ that will do as the number of cycles}$

So one of the solutions is 0.28869 to 5 decimal places.

I can not find the seed value that returns 1.21 as a solution

Note that in this format $3 {x}^{3} = + 7$ is an excluded value