Question

prove that the expressions n^2-3n+1/n-1 is not a prime number for all n

Answer 1

SOLUTION

TO PROVE

The below expressions is not a prime number for all n

$\displaystyle \sf{ \frac{ {n}^{2} - 3n + 1 }{n - 1} }$

EVALUATION

Here the given expression is

$\displaystyle \sf{ \frac{ {n}^{2} - 3n + 1 }{n - 1} }$

The above expression is undefined when n = 1

So the expression is not defined for all values of n

Moreover if we take n = 3 then we get

$\displaystyle \sf{ = \frac{ {3}^{2} - 3 \times 3 + 1 }{3 - 1} }$

$\displaystyle \sf{ = \frac{9- 9 + 1 }{2} }$

$\displaystyle \sf{ = \frac{ 1 }{2} }$

Which is not a prime

Hence

$\displaystyle \sf{ \frac{ {n}^{2} - 3n + 1 }{n - 1} }$

is not a prime number for all n

Hence proved

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