2022/074) if a and b are roots of $x^2-3x+1=0$ then find the value of $(a^a + b^b)(a^b+ b^a)$

 We are given f a and b are roots of $x^2-3x+1=0$

so $a + b = 3\cdots(1)$
$ab=1\cdots(2)$2

now $ $(a^a + b^b)(a^b+ b^a)$$

= $a^{a+b} + (ab)^a + (ba)^b  b^(b+a)$

= $a^3 + 1 + 1 + b^3$ putting the value of a+b and ab from (1) and (2)

=$a^3 + b^3 + 2$

= $(a+b)^3 - 3ab(ab+b) + 2$ using formula for $a^3+b^3$

= $3^3 - 3 . 1 . 3 + 2 = 20$ putting values from (1) ansd (2)