Question

What is an approximate solution to this equation? 4/x-5=√x+3+2



A. 3.73

B. 5.81

C. 4.97

D. -0.80

Answer 1

The approximate solution to the equation $\dfrac{4}{x - 5} = \sqrt{x + 3} +2$ found using

the Newton-Raphson method is option B.

B. 5.81

How can the Newton-Raphson method be used?

The given function is presented as follows;

$\dfrac{4}{x - 5} = \mathbf{ \sqrt{x + 3} +2}$

Which gives;

$\dfrac{4}{x - 5} -2= \sqrt{x + 3}$

$\left(\dfrac{14-2\cdot x}{x-5} \right)^2 = \sqrt{x+3} ^2 = x+3$

$\mathbf{\dfrac{4\cdot x^2 - 56 \cdot x + 196}{x^2-10\cdot x + 25}} = x + 3$

Therefore;

$\mathbf{\dfrac{4\cdot x^2 - 56 \cdot x + 196}{x^2-10\cdot x + 25} - (x + 3)} = 0$

$\dfrac{- x^3 + 11 \cdot x^2 - 51 \cdot x + 121}{x^2-10\cdot x + 25} = 0$

x³ - 11·x² + 51·x - 121 = 0

Using the Newton Raphson method, with x₀ = 6, we have;

$x_1 = x_0- \dfrac{x^3 - 11 \cdot x^2 + 51 \cdot x - 121}{3 \cdot x^2 - 22 \cdot x + 51}$

Which gives;

$x_1 = 6- \dfrac{6^3 - 11 \times 6^2 + 51 \times 6 - 121}{3 \times 6^2 - 22 \times 6 + 51} \approx \mathbf{ 5.81}$

The correct option is B. 5.81

Learn more about the roots polynomial functions here:

https://brainly.com/question/25956931