Question

How many extraneous solutions does the equation below have?

Answer 1

Answer:

A. 0

Step-by-step explanation:

How many extraneous solutions does the equation below have?

StartFraction 9 Over n squared + 1 EndFraction = StartFraction n + 3 Over 4 EndFraction

0

1

2

3

Answer 2

Answer:

We can say that the given equation has no extraneous solutions.

The correct option is A.) 0

Step-by-step explanation:

the given equation is $\frac{9}{n^{2} +1} = \frac{n+3}{4}$

this equals to $36 = (n^{2} +1)(n+3) = n^{3} + 3n^{2} + n + 3$

therefore $n^{3} +3n^{2} +n+3 = 36 \hspace{0.3cm}\Rightarrow \hspace{0.3cm}n^{3} +3n^{2} +n-33=0$

Solving the equation through Newton-Raphson method we get n  $\approx$  2.3845.

We can say that the given equation has no extraneous solutions.