Question

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 1

A. 0

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

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

The correct option is A.) 0

Explanation:

the given equation is
`(9)/(n^(2) +1) = (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.