If n3-9 n2-26 n-24-2 b- then the value of n is where n - N and b is a prime numberA- 3B- 4C- 6D- 5

The correct option is D 5n^3 9n^2+26n 24=2b Factorizing the equation ⇒ (n 2)(n 3)(n 4)=1×2× b Since, b is a prime number so it cannot have more than 2 factors. ...

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Standard XII

Mathematics

AM,GM,HM Inequality

If n3-9 n2+26...

Question

If $n^{3} - 9 n^{2} + 26 n - 24 = 2 b,$ then the value of $n$ is
(where $n \in N$ and $b$ is a prime number)

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Solution

The correct option is C $5$
$n^{3} - 9 n^{2} + 26 n - 24 = 2 b$
Factorizing the equation
$\Rightarrow (n - 2) (n - 3) (n - 4) = 1 \times 2 \times b$
Since, $b$ is a prime number so it cannot have more than $2$ factors.
So, here $n - 4 = 1$
(smallest factor will be $1$ )
and $n - 3 = 2$
$\Rightarrow n = 5$

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If n3−9n2+26n−24=2b, then the value of n is (where n∈N and b is a prime number)

The correct option is C 5n3−9n2+26n−24=2b Factorizing the equation ⇒(n−2)(n−3)(n−4)=1×2×b Since, b is a prime number so it cannot have more than 2 factors. So, here n−4=1 (smallest factor will be 1) and n−3=2 ⇒n=5

If $n^{3} - 9 n^{2} + 26 n - 24 = 2 b,$ then the value of $n$ is
(where $n \in N$ and $b$ is a prime number)