Question

A positive number N= (n+4)(n+5)(n+6)(x+7) is not divisible by which of the following
A)3
B)4
C)5
D)6

Answer 1

Answer:

N= (n+4)(n+5)(n+6)(n+7)

⇒ N = [n(n+5) +4(n+5)][(n(n + 7)+6(n+7)

⇒ N = n² + 5n + 4n + 20 × n² + 7n + 6n + 42

⇒ N = n⁴ + 9n + 840 + 13n

⇒ N = n⁴ + 117n + 840

$\large \rm⇒ \: \dfrac{n}{n} = {n}^{4} + 117 + 840$

$\large \rm⇒ \: {n}^{4} = 957$

$\large \rm⇒ \: {n}^{ } = \sqrt[4]{ 957}$

therefore 5 ( approx)

Answer 2

Answer:

$\begin{gathered}{\underline{\underline{\maltese{{\textsf{\textbf{\purple{Solution: }}}}}}}}\end{gathered}$

N= (n+4)(n+5)(n+6)(n+7)

⇒ N = [n(n+5) +4(n+5)][(n(n + 7)+6(n+7)

⇒ N = n² + 5n + 4n + 20 × n² + 7n + 6n + 42

⇒ N = n⁴ + 9n + 840 + 13n

⇒ N = n⁴ + 117n + 840

$\large \rm⇒ \: \dfrac{n}{n} = {n}^{4} + 117 + 840$

$\large \rm⇒ \: {n}^{4} = 957$

$\large \rm⇒ \: {n}^{ } = \sqrt[4]{ 957}$

therefore 5 ( approx)