So how do we approach this Q? one way is to have it as a function of (x) only and express it as
g(x) = x^x + (1-x)^(1-x) and then try to find the f’(x) =0 and solve the usual way… and you can see you’re headed to trouble. So let’s try another way!
Q: Lets a and b be real numbers for which the equation x⁴ + ax³ + bx² +ax +1 = 0 has at least one real solution. For all such pairs (a, b), find the minimum value of a²+b².
A: As there is symmetry is the coefficients, first consider the eq. y = x+ 1/x and…