The two positive integer solutions of the equation $x^2 - mx + n = 0$ are $k$ and $t$, where $m$ and $n$ are both prime numbers and $k > t$. what is the value of $m^n + n^m + k^t + t^k$?

Since k and t are roots of x² - mx + n = 0,

0 = (x - k)(x - t) = x² - (k+t)x + kt = x² - mx + n

Equating respective coefficients,

m = k + t   and  n = kt

If n is prime we have one of k and t must be a unit ±1.  Since we're told they're positive, the smallest must be +1, so we conclude

t = 1

So

n = kt = k

We're told m is prime

m = k + t = n + 1

m and n are consecutive and prime.  The only consecutive primes are 2 and 3.  Our solution is

k = 2, n = 2, m = 3, t = 1

We're inexplicably asked for the symmetric quantity

We compute

3² + 2³ + 2 + 1² = 9 + 8 + 2 + 1 = 20

20

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation:

the correct answers i think are b. and d.

give me brainliest if it is correct!