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Alex777 [14]
2 years ago
13

How many extraneous solutions does the equation below have? StartFraction 9 Over n squared 1 EndFraction = StartFraction n 3 Ove

r 4 EndFraction.
Mathematics
1 answer:
BigorU [14]2 years ago
5 0

The equation has one extraneous solution which is n ≈ 2.38450287.

Given that,

The equation;

\dfrac{9}{n^2+1} =\dfrac{n+3}{4}

We have to find,

How many extraneous solutions does the equation?

According to the question,

An extraneous solution is a solution value of the variable in the equations, that is found by solving the given equation algebraically but it is not a solution of the given equation.

To solve the equation cross multiplication process is applied following all the steps given below.

\rm \dfrac{9}{n^2+1} =\dfrac{n+3}{4}\\\\9 (4) = (n+3) (n^2+1)\\\\36 = n(n^2+1) + 3 (n^2+1)\\\\36 = n^3+ n + 3n^2+3\\\\n^3+ n + 3n^2+3 - 36=0\\\\n^3+ 3n^2+n -33=0\\

The roots (zeros) are the  x  values where the graph intersects the x-axis. To find the roots (zeros), replace  y

with  0  and solve for  x. The graph of the equation is attached.

n  ≈  2.38450287

Hence, The equation has one extraneous solution which is n  ≈  2.38450287

For more information refer to the link.

brainly.com/question/15070282

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