Question

x^4+x^2+1 is a prime number . find the number of values of x . x € n​

Answer 1

The correct question may be like:

x^4+x^2+1 is a prime number . find the number of values of x . x € n

"Answer: There are no values of x in N that make x^4+x^2+1 a prime number.

To check if (x^4+x^2+1) is a prime number, we can use the fact that if a number is not prime, it can be factored into smaller factors. We can try to factor (x^4+x^2+1) using the difference of squares formula:

$x^4+x^2+1 = (x^2)^2 + 2(x^2)(1) + 1 - (x^2)(1)^2 - 1$

$= (x^2+1)^2 - x^2$

$= (x^2+x+1)(x^2-x+1)$

Therefore,$x^4+x^2+1$ is not a prime number unless one of the factors, $x^2+x+1$ or $x^2-x+1$, is equal to 1. However, both of these factors are quadratic expressions and can never be equal to 1 for any integer value of x. Therefore, there are no values of x in N that make $x^4+x^2+1$ a prime number."

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